NOTES: TRANSFORMATIONS

Transcription

1 TABLE OF CONTENT Plotting Points On A Coordinate Plane. Transformations. Translation. Reflections. Rotations Dilations. Congruence And Similarity.. Multiple Transformations In A Coordinate Plane. Parallel Lines And Transversals.... Triangles...

2

3 NOTES: TRANSFORMATIONS A transformation is an operation on a geometric figure that preserves a one-to-one correspondence between every point in the original figure and a new point on the transformed image of the figure. In friendlier terms, a transformation is simply The is the original location of a point or figure. The image occurs after a transformation takes place, and is signified with an accent mark beside the new point (Prime Notation) Example: There are four types of transformations: Translation Reflection Rotation Dilation

4 NOTES: TRANSLATIONS Translation: Creates a new image of a geometric figure by sliding it to the left, right, up or down to a new location. Example: When translating (sliding) a figure on a coordinate plane the figure can move vertically (up or down), horizontally (left or right), or a combination of the two. It is important to remember that a translation DOES NOT change the size or orientation of the figure, simply its location Let s try a few! PREIMAGE B (-5, 1) C (-5, 4) D (2, 1) Move 5 units to the right PREIMAGE N (-3, 3) O (-5, -2) P (3, 1) Move 3 units down PREIMAGE X (-6, -6) Y (-4, 2) Z (1, 3) Move x + 4, y -4 PREIMAGE J (6, 2) K (-3. -3) L (2, -1) Move three units to the left and 2 units up 1. If point A is at -4, 1 and translates 7 units to the right, which quadrant will A be located? 2. If point A moved 3 units down, which quadrant will A be located? 3. If A is located at (2, -6), what translation took place? (It looks tricky, but I PROMISE you it s not!) 4. B is located at (3, 6). The translation that took place was (x - 2, y + 10). In which quadrant is the preimage located?

5 NAME DATE PERIOD TRANSLATIONS IN A COORDINATE PLANE PRACTICE 1. A (2, 4), B (-1, 3), C (2,-3) Translation: 4 units to the right and 5 units down A B C 2. A (1, 3), B (-2, 6), C (0, 0) Translation: 6 units to the right and 3 units up A B C

6 What does a left or right movement change? What does an up or down movement change? What will happen to a figure if the translation applied is (x + 3, y 4)? Describe the transformation that is represented by the following. (x + 3, y) (x 2, y + 4) (x, y - 5) What are the coordinates of the preimage if the image was translated 4 units to the right and 4 units down? Preimage C J K M What are the coordinates of the preimage if the image was translated (x 3, y)? Preimage C J K M In your own words (complete sentences), explain translations and their effect(s) on geometric figures.

7 NAME DATE PERIOD EXIT TICKET: TRANSLATIONS What are the coordinates of X when triangle WXY is translated 2 units down and 5 units to the right? Parallelogram ABCD was translated to parallelogram A B C D. How many units and in which direction were the x- coordinates of parallelogram ABCD moved? A. 3 units to the right B. 3 units to the left A. 1, 3 B. 3, 1 C. 4, 6 D. 6, 4 Figure EFGH in the coordinate plane has vertices at (-5, 2), (-5, -2), (-1, -2), and (-1, 2). C. 7 units to the right D. 7 units to the left Which of the following does not represent a translation? A. B. C. D. If the figure is translated 5 units to the right and 2 units up, what are the coordinates of E F G H? A. (0, 4), (0, 0), (4, 0), (4, 4) B. (-3, 7), (-3, 3), (1, 3), (1, 7) C. (-10, 0), (-10, 4), (-6, -4), (-6, 0) D. (-7, -3), (-7, -7), (-3, -7), (-3, -3)

8

9 NOTES: REFLECTIONS Reflection: Creates a mirror image of a geometric figure when each point is the same distance from the line of reflection. Examples: A reflection occurs when your image is flipped across a line of reflection. To create an exact replica, the preimage and corresponding image points must be equal distance from the line of reflection. It is important to remember that a reflection DOES NOT change the size of the figure, simply its orientation and location Let s try a few! Preimage B (-5, 1) C (-5, 4) D (2, 1) Preimage N (-3, 3) O (-5, -2) P (3, 1) Reflect across the x-axis Reflect across the y-axis

10 Plot the preimage N (-4, 1), O (-2, 6), P (-1, 2). 1. If reflected across the x-axis, in which quadrant will the image be located? A. What are the coordinates of the image created by the transformation? 2. If the preimage is reflected across the y-axis, in which quadrant will the image be located? A. What are the coordinates of the image created by the transformation? 3. If the preimage is reflected across x = y, what are the coordinates of the image?

11 NAME DATE PERIOD REFLECTIONS IN A COORDINATE PLANE PRACTICE

12

13 NAME DATE PERIOD REFLECTIONS PRACTICE 1. How do the coordinates change when an object is reflected across the x-axis? 2. How do the coordinates change when an object is reflected across the y-axis? 3. (4, 3) reflected across the x-axis 4. (-2, 1) reflected across the y-axis 5. (0, 0) reflected across the y-axis 6. (-5, -6) reflected across the x-axis 7. (0, 9) reflected across the x-axis 8. (7, 0) reflected across the y-axis 9. A (2, 4), B (-1, 3), C (2,-3) Reflection: across the x-axis A B C 10. A (1, 3), B (-2, 6), C (0, 0) Reflection: Across the y-axis A B C 11. A (0, 0), B (5, 2), C (4, 4) Reflection: over the line y = x A B C 12. Describe the transformation that is represented by the given rule. A. (x, y) = (-x, y) B. (x, y) = (-x, -y) C. (x, y) = (x, -y)

14 NAME DATE PERIOD EXIT TICKET: REFLECTION Which of the following is a single reflection of figure N over the y-axis to form N? Which figure shows the triangle below reflected over the x-axis, then reflected over the y-axis?

15 NOTES: ROTATION Rotation: Create a new image of a geometric figure by rotating (turning) it clockwise or counter-clockwise For the purposes 8 th grade content, we will focus on rotations of 90 o increments the origin of the coordinate graph The origin is the point where the x and y-axis intersect. Clockwise rotates the figure around the coordinate plane in a leftward motion Counter-clockwise rotates the figure around the coordinate plane in a rightward motion It is important to remember that a rotation DOES NOT change the size of the figure, simply its orientation and location

16 Preimage B (-5, 1) C (-5, 4) D (2, 1) Preimage N (-3, 3) O (-5, -2) P (3, 1) Rotate 90 o clockwise Rotate 180 o counterclockwise Plot the preimage N(-4, 1), O(-2, 6), P(-1, 2). 1. If rotated 270 o clockwise, in which quadrant will the image be located? a. What are the coordinates of the image created by the transformation? 2. If the preimage is rotated 180 o, in which quadrant will the image be located? a. What are the coordinates of the image created by the transformation?

17 NAME DATE PERIOD ROTATIONS IN A COORDINATE PLANE Rotate 180 o clockwise Rotate 180 o counterclockwise A (-2, 4) B (-5, 1) C (-1, 1) A (-2, 4) B (-5, 1) C (-1, 1) A B C A B C Rotating 180 o clockwise is the same as rotating 180 o clockwise or, the pre-image coordinates When rotating Rotate 90 o clockwise Rotate 270 o counterclockwise A (3, 5) B (5, 1) C (1, 2) A (3, 5) B (5, 1) C (1, 2) A B C A B C

18 Rotating 90 o clockwise is the same as rotating clockwise or, the pre-image coordinates When rotating 90 o Rotate 270 o clockwise Rotate 90 o counterclockwise A (3, -1) B (1, -4) C (5, -5) A (3, -1) B (1, -4) C (5, -5) A B C A B C Rotating 90 o counterclockwise is the same as rotating When rotating 90 o counterclockwise or the pre-image coordinates Let s use our observations to determine the new coordinates for the following coordinates after the stated rotation. Try to use rules that we discovered first, and check your solution with patty paper. Point A at (-6, 3) rotated 90 o clockwise Point B at (4, 3) rotated 180 o Point C at (-1, -7) rotated 90 o counterclockwise

19 NAME DATE PERIOD EXIT TICKET: ROTATIONS 1. If triangle ABC is rotated 180 o about the origin, what are the coordinates of A? A. (-5, -4) B. (-5, 4) C. (-4, 5) D. (-4, -5) 2. A figure is located in quadrant I. It is rotated 180 o. In which quadrant will the new image be located? A. Quadrant I B. Quadrant II C. Quadrant III D. Quadrant IV 3. Rotating a figure around the origin will change. A. The size, location, and orientation B. Only the location C. The size and location D. The orientation and location E. The size and orientation F. Only the orientation 4. Joanne and Christopher are designing a quilt. They start by creating a triangle shape in the lower left quadrant as shown to the right. They transform it by rotating the triangle shown above 90 o clockwise about the origin. What does the new design look like? A. B. C. D.

20

21 NOTES: DILATIONS Dilation: Create a larger or smaller image of a geometric figure. The amount of increase or decrease in the size of the geometric figure is called the scale factor. All points of the preimage are multiplied by the scale factor to determine the new coordinates of the image. The figure will get larger when the scale factor is greater than 1 The figure will get smaller when the scale factor is less than 1 It is important to remember that a dilation DOES NOT change the orientation of the figure, simply its size and location Examples: Scale factor of 3. Since the scale factor is greater than 1 the figure will enlarge Scale factor of ½. Since the scale factor is less than 1 the figure will decrease in size. How do you determine the new coordinates when given the scale factor? Simply multiply each coordinate by the value to get the new coordinates. If you are given the coordinates for a figure: (2, 5), (1,2 ), (8, 4) and the scale factor is 2, then multiply each x and y value by 2 to get your new set of coordinates- (4, 10), (2, 4), (16, 8)

22 IT S THAT EASY!!! Let s try it! The preimage N(-4, 2), O(-2, 6), P(-2, 2). 1. If the scale factor is 1.5 what will happen to the figure? 2. If the scale factor is ¾ what will happen to the figure? 3. If the preimage is dilated by a scale factor of 3, what are the coordinates of the new image? 4. If the preimage is dilated by a scale factor of ½, what are the coordinates of the new image? What is the scale factor used to make the transformation? Dilate by ½ What is the scale factor used to make the transformation? U (-2, -1) U (-4, -2) V (0, 2) V (0, 4) W (2, -2) W (4, -4)

23 NAME DATE PERIOD DILATION IN A COORDINATE PLANE PRACTICE 1. In Math, the word dilate means to or 2. Scale factor is a figure. 3. If a scale factor is less than 1, then your figure gets. 4. If your scale factor is less than 100%, then your figure gets. 5. If a scale factor is greater than 1, then your figure gets. 6. If your scale factor is greater than 100%, then your figure gets. 7. Can you have a scale factor LESS than 1?.

24

25

26 The table below shows the coordinates of triangle RST and the coordinates of R in triangle R S T. Triangle R S T is a dilation of triangle RST. Triangle RST Triangle R S T R (-2, -3) R' (-6, -9) S (0, 2) S T (2, -3) T Part A What are the coordinates of point S and point T? S T Part B On the grid below, draw triangle RST and triangle R S T.

27 NOTES: SEQUENCE OF TRANSFORMATIONS How do you boil an egg? How would you make a call from a newly purchased cell phone that's in the box? (Give EXPLICIT directions.) How do you solve 2x - 5 = 17? SEQUENCE - a number of things, actions, or events that happen in a specific order The four transformations and their action: In this lesson we will apply the knowledge we have acquired about transformations to determine the outcome of a sequence of transformations. Let s try the first two together!

28 NAME DATE PERIOD a. Plot the pre-image, Quadrilateral ABCD: A(-6,4), B(-5,6), C(-4,4), D(-5,2) SEQUENCE OF TRANSFORMATIONS PRACTICE b. Then, reflect the quadrilateral across the x-axis creating image A B C D c. Then, translate the image A B C D (x,y) (x+3, y-5) to create image A B C D a. Plot the pre-image, Pentagon EFGHI: E(-5,1), F(-3,3), G(-1,3), H(1,1), I(-2,0) b. Then, reflect the pentagon across the y-axis creating image E F G H I c. Then, rotate E F G H I 90 counterclockwise about the origin to create image E F G H I

29 a. Plot the pre-image, Pentagon JKLMN: J(2,4), K(3,7), L(4,5), M(5,7), N(6,4) b. Then, translate the pentagon (x,y) (x-4, y-2) creating image J K L M N c. Then, reflect J K L M N across the x-axis to create image J K L M N a. Plot the pre-image, Quadrilateral OPQR: O(1,-6), P(3,-5), Q(7,-1), R(5,-2) b. Then, translate the quadrilateral (x,y) (x-6, y+7) creating image O P Q R c. Then, rotate O P Q R 180⁰ clockwise about the origin to create image O P Q R

30 a. Plot the pre-image, Quadrilateral STUV: S(-2,-2), T(-5,-6), U(-6,-6), V(-6,-5) b. Then, rotate the quadrilateral 90⁰ clockwise about the origin creating image S T U V c. Then, translate S T U V (x,y) (x+8, y+1) creating image S T U V a. Plot the pre-image, Triangle WXY: W(0,4), X(-2,-2), Y(1,-3) b. Then, rotate the triangle 270 clockwise about the origin creating the image W X Y c. Then, reflect W X Y across the y-axis creating image W X Y

31 NOTES: CONGRUENCE AND SIMILARITY QUESTIONS: If you look you are standing directly in front of a mirror looking at your image what differences do you see if any? Is it the same as what s actually there? Does the size or shape change? What about a 4 x 6 photo of yourself? Is it the same as what s actually there? Does the size or shape change? The differences between your responses can easily be explained with similarity and congruence. CONGRUENCE Congruence is defined as exactly equal in size and shape. This means all sides and angles are equal. The universal symbol for congruence Let s look at an example. Let s determine if triangle ABC is congruent to triangle A B C. To do this we need to determine if the points, sides, and angles are exactly same.

32 Let s try several problems together! Mark all congruent sides and angles in the figures below.

33 SIMILARITY Similarity is defined as having the same shape, having proportional corresponding sides, and corresponding angles that are equal When two polygons are similar, we can write a similarity statement using the symbol ~ Similarity can be determined by finding the scale factor used to make the dilation. If the same scale factor is used for each side, it is the EXACT same shape, AND all corresponding angles are congruent, then the figures are similar. Let s try other examples.

34 A giraffe is 18 feet tall and cast a shadow of 12 feet. Corry casts a shadow of 4 feet. How tall is Corry? A flagpole cast a shadow 28 feet long. A person standing nearby casts a shadow 8 feet long. If the person is 6 feet tall, how tall is the flagpole?

35 NAME DATE PERIOD CONGRUENCE AND SIMILARITY PRACTICE Write a statement that indicates that the triangles in each pair are congruent Mark the angles and sides of each pair of triangles to indicate that they are congruent Which pieces of the puzzle are congruent? Explain your answer:

36 In the diagram MLK JET. Complete the statements below. Find the value of the missing side or sides. Two rectangles are similar. The first is 4 in. wide and 15 in. long. The second is 9 in. wide. Find the length of the second rectangle. The scale of a map of Tennessee is 1 inch: 25 miles. If you measure the distance from Nashville to Knoxville as 7.2 in, approximately how far is Nashville from Knoxville?

37 NAME DATE PERIOD EXIT TICKET: SIMILARITY 1. Which of the following is not a characteristic of similar figures? 2. Are the figures below similar? Explain. A. Proportional sides B. Equal angle measurements C. Same shape D. Congruent side lengths 3. Explain why figures A and B are similar. 4. If the figures below are similar, what is true about the angles of the smaller figure?

38 5. Each pair of rectangles below ae similar. Calculate the values of dimension x.

39 NAME DATE PERIOD SIMILARITY AND CONGRUENCE 1. Check off all the correct conditions that make 2 triangles congruent: same shape same size corresponding angles equal corresponding sides equal same orientation 2. Check off all the correct conditions to make 2 triangles similar: same shape same size corresponding angles equal corresponding sides equal same orientation 3. Check of the condition that makes the statement true for Triangle 3. Triangle 1 Triangle 2 Triangle 3 GIVEN: Triangle 1 was flipped to create Triangle 2. Triangle 3 is: Triangle 2 was then increased in size proportionally to create Triangle 3. congruent to Triangle 1. similar to Triangle 1. neither congruent nor similar to Triangle 1. Explain why. 4.

40 5. Determine if each pair of polygons are similar. If so, write the similarity statement and the similarity ratio. 6. In the given triangles below, KLM ~ XYZ. Find the missing length. 7. In the given triangles below, ABC ~ DEF. Find the missing length. 8. Are these triangles similar? In the given triangles below, MNO ~ XYZ. Find the missing length.

41 NAME DATE PERIOD Living Room Furniture Layout (Before) After moving into a new apartment, the Harrisons decided on the simple layout below for their living room. Find the four corner points of each piece of furniture in the diagram below: Piece of furniture Top Left Coordinates Top Right Coordinates Bottom Left Coordinates Bottom Right Coordinates End Table #1 Sofa End table #2 Coffee table Bookcase #1 TV stand Bookcase #2

42 Living Room Furniture Layout (Transformation) The Harrisons decide that they want to transform their boring living room. -They buy a new sofa that is congruent to their current sofa. It is placed in the position of the original sofa reflected across the x axis. -Bookcase #1 is rotated 90 o clockwise, and moved 2 units up and 2 units right. -Bookcase #2 is rotated 90 o counterclockwise and moved 2 units to the left and 4 units up. -TV stand is rotated 90 o counterclockwise and translated 3 units to the left. -Coffee table is dilated by a scale factor of 1/3. -End table #1 is rotated 180 o. -End table #2 is reflected across the y axis. Piece of furniture Top Left Coordinates Top Right Coordinates Bottom Left coordinates Bottom Right Coordinates End Table #1 Sofa End table #2 Coffee table Bookcase #1 TV stand Bookcase #2

43 SUPPLEMENTARY ANGLES VERTICAL ANGLES ALTERNATE EXTERIOR ANGLES COMPLEMENTARY ANGLES CORRESPONDING ANGLES ALTERNATE INTERIOR ANGLES

44 Two or more s are COMPLEMENTARY if the sum of their measures is. What is the measure of the missing? Angles in locations on parallel lines intersected by a transversal are CORRESPONDING s. Name the corresponding s Angles that are formed on sides of the transversal and the parallel lines are ALTERNATE INTERIOR s. Name the alternate interior s. Two or more s are SUPPLEMENTARY if the sum of their measure is. Which angles are supplementary s? A pair of VERTICAL s are formed by an of two lines. Which are vertical s? Angles that are formed on sides of the transversal and the parallel lines are ALTERNATE EXTERIOR s. Name the alternate exterior s.

45

46

47 NAME DATE PERIOD CLASSIFYING ANGLES PRACTICE Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior CHALLENGE PROBLEM CHALLENGE PROBLEM

48 Identify each pair of given angles by classification and find the measure of each angle indicated Solve for x

49 NAME DATE PERIOD FINDING THE MEASURE OF MISSING ANGLES Find the value of the variable AND the angle(s).

50

51 NAME NAME NAME NAME FINDING MISSING MEASURES USING ANGLE RELATIONSHIPS PUZZLE (SOLUTIONS) x = A = B = C = D = E = F = G = H = J = K = L = M = N = O = P = Q = R = S = T = U = W = Y = ANGLE RELATIONSHIP

52

53 NOTES: TRIANGLES TYPES OF TRIANGLES There are six types of triangles that you have become familiar with over the years. Let s review them. Right Triangle Obtuse Triangle Acute Triangle Three of the types of triangles are identified by their angles RIGHT TRIANGLE These triangles have a 90 o angle Equilateral Triangle Isosceles Triangle Scalene Triangle Three of the types of triangles are identified by their sides. Isosceles Triangles Triangle has TWO equal sides OBTUSE TRIANGLE These triangles have an angle greater than 90 o Equilateral Triangles Triangle has ALL equal sides ACUTE TRIANGLE All angles in this type of triangle are less than 90 o Scalene Triangles Triangle has NO equal sides

54 INTERIOR ANGLES OF A TRIANGLE There are 3 interior angles of a triangle. These three angles have an angle sum of 180 o. EXTERIOR ANGLES Exterior angles are created by one side of a triangle and the extension of the adjacent side of the triangle. These exterior angle measures can be determined using the Exterior Angle Theorem which states that the measure of an exterior angle is equal to the sum of the remote, or OPPOSITE, two interior angles. Let s Practice!! Identify the type of triangle by its sides and angles, than find the missing values.

55 NAME DATE PERIOD TRIANGLES PRACTICE Find the measure of the unknown interior angle for each triangle. Find the unknown exterior angle for each triangle.

56 Find the measures of the missing angles and x. (CHALLENGE PROBLEMS!) Use the space below to show work!

57 NAME DATE PERIOD Culminating Task: Design Your City You are working for a Design Firm to accurately create a city design plan in the form of a map. No two buildings can occupy the exact same space. Since you are doing this for a company, it must be neat! Use a ruler to draw straight lines, please no free-hand- drawing of these or points will be deducted. City Designers must accurately draw parallel, perpendicular, and transversal lines to create your city map design. To start your city: Your city must have a name Your city must have at least 3 parallel streets (each street must be named) Your city must have at least 1 transversal street (each street must be named) Your city must have at least 1 perpendicular street (each street must be named) To complete your city: Place the following buildings correctly based on the directions below. All buildings must be given names using signs either on or near the building. Find a pair of alternate interior angles. Draw a pet shop and a school on the alternate interior angles. Find a pair of corresponding angles. Draw a bank and a post office on the corresponding angles. Additionally, the bank must be a dilation of the post office with a scale factor 2. Find a pair of alternate exterior angles. Draw a grocery and a movie theater on these angles. Find angles that are supplementary (or form a linear pair). Draw a restaurant and a gas station on these angles. Find a pair of vertical angles. Draw a fire department and hospital on the vertical angles. Additionally, the hospital should be a reflection of the fire department. Draw the line of reflection as a dotted line.

58 Once your city is fully designed, answer the following questions: 1. What sequence of transformations would take your grocery store to the location of your restaurant? Your description should be transformations relative to your street names. 2. Add a bowling alley to your city that is congruent to your post office. Prove their congruence using a sequence of transformations. 3. Add a gym to your city that is similar to your pet shop. Prove their similarity using a sequence of transformations. 4. What 3 streets form the parallel lines and transversal that make your grocery store and movie theatre alternate exterior angles? Explain using pictures and/or words.

59 Achieveme nt Level 7-8 Criteria A & Criteria D Criteria A: Knowing & Understanding Descriptor The student is able to: i. select appropriate mathematics when solving challenging problems in both familiar and unfamiliar situations. ii. apply the selected mathematics successfully when solving these problems iii. generally solve these problems correctly. Criterion D: Applying Mathematics in real-life contexts Descriptor The student is able to: i. identify the relevant elements of the authentic reallife situation. ii. select appropriate mathematical strategies to model the authentic real-life situation. iii. apply the selected mathematical strategies to reach a correct solution The student is able to: i. select appropriate mathematics when solving challenging problems in familiar situations. ii. apply the selected mathematics successfully when solving these problems iii. generally solve these problems correctly. The student is able to: i. select appropriate mathematics when solving more complex problems in familiar situations. ii. apply the selected mathematics successfully when solving these problems iii. generally solve these problems correctly. iv. explain the degree of accuracy of the solution. v. explain whether the solution makes sense in the context of the authentic real-life situation. The student is able to: i. identify the relevant elements of the authentic reallife situation. ii. select adequate mathematical strategies to model the authentic real-life situation. iii. apply the selected mathematical strategies to reach a valid solution to the authentic real-life situation. iv. describe the degree of accuracy of the solution. v. discuss whether the solution makes sense in the context of the authentic real-life situation. The student is able to: i. identify the relative elements of the authentic real-life situation ii. select, with some success, adequate mathematical strategies to find a solution to model the authentic reallife situation iii. apply mathematical strategies to reach a solution to the authentic real-life situation 1-2 The student is able to: i. select appropriate mathematics when solving simple problems in familiar situations. ii. apply the selected mathematics successfully when solving these problems iii. generally solve these problems correctly. 0 The student does not reach a standard described by any of the descriptors below. iv. describe whether the solution makes sense in the context of the authentic real-life situation The student is able to: i. identify some of the elements of the authentic reallife situation ii. apply mathematical strategies to find a solution to the authentic real-life situation, with limited success The student does not reach a standard described by any of the descriptors below.

60 STRUCTURE (2 points each) Name of City clearly labeled At least 3 parallel streets clearly labeled At least 1 street perpendicular to the others At least 1 transversal street /8 LOCATIONS (2 points each) A pet shop and a school (alternate interior angles) A bank and a post office (corresponding angles) A bank and a post office (dilation scale factor 2) A grocery and a movie theatre (alternate exterior) A restaurant and a gas station (linear pair or supplementary) A fire department and a hospital (vertical angles) /14 The hospital is a reflection of the fire department (line of reflection) QUESTIONS (24 points each) /24 OTHER (2 points total) Neatness (labeling is clear, use of appropriate paper, lines are straight) Creativity Effort (use of color, other additions to city) TASK TURNED IN BEFORE OR ON DEADLINE (2 points total) -2 points per day past deadline TOTAL POINTS /2 /2 /50

61 NAME BELL RINGER #1 Label the x and y axis on the graph below. Plot the point (3, 5) on the graph. Move the point 6 units to the left. What are the new coordinates? PERIOD Which quadrant are the new coordinates located in? Solve the following. 3 5 = = -6 (-8) = -8 + (-4) =

62

63 NAME BELL RINGER #2 DATE Translate the following coordinates 3 units to the right and 2 units down. Preimage (-5, 5) (-6, 2) (-1, 1) Image (, ) (, ) (, ) Which quadrant does the shape move to? The translation (x+ 6, y - 3) means: A. Move 6 up and 3 to the left B. Move 6 to the left and 3 down C. Move 6 down and 3 to the left D. Move 6 to the right and 3 down If the coordinates of (4, 7) move 9 to the right and 8 down, what are the new coordinates?

64

65 NAME DATE PERIOD BELL RINGER #3 1. A trapezoid with vertices W (-1, 2), X (3, 2), Y (2, -1), and Z (-2, -1) is reflected on the x-axis. What are the coordinates of the vertices of the new image? A. W (1, 2), X (-3, 2), Y (-2, -1), Z (2, -1) B. W (-1, -2), X (3, -2), Y (2, 1), Z (-2, 1) C. W (2, -1), X (2, 3), Y (-1, 2), Z (-1, -2) D. W (-2, -1), X (-2, 3), Y (1, 2), Z (1, -2) 2. If triangle XYZ was translated 4 to the left and 2 up, where would the image of the triangle be located? a) image "a" b) image "b" c) image "c" d) image "d" 3. Which diagram shows the image of triangle CAB after the translation? a. 4 units right, 2 units down b. 7 unit right c. 5 units right, 2 units down d. 3 units right 4. The vertices of a figure and its translation image are given. What is the translation? Figure: A (-2, -1), B (1, 1), C (3, -2), D (0, -4) Image: A (0, 2), B (3, 4), C (5, 1), D (2, -1)

66

67 NAME DATE PERIOD BELL RINGER CONGRUENT FIGURES These shapes have been drawn on a grid of centimeter squares. (a) (i) Write down the letters of a pair of shapes that are congruent. (ii) Write down the letters of a different pair of shapes that are similar. (b) Find the perimeter of shape D.

68

69 NAME DATE PERIOD BELL RINGER CONGRUENT FIGURES Here are some rectangles on a grid of centimeter squares. (a) Find the area of rectangle G. (b) Find the perimeter of rectangle B. Two of the rectangles are congruent. (c) Write down the letters of these two rectangles. Rectangle F is an enlargement of rectangle B. (d) Write down the scale factor of the enlargement.

70