1) y = 2x 7 2) (-2, 3) ( 3, -1) 3) table. 4) y 5 = ½ ( x 4) 5) 2x + 4y = 7 6) y = 5 7) 8) 9) (-1, 5) (0, 4) 10) y = -3x 7. 11) 2y = -3x 5 12) x = 5

Transcription

1 I SPY Slope! Geometr tetbook 3-6, pg 165 (), pg 172 (calculator) Name: Date: _ Period: Strategies: On a graph or a table rise ( Δ) Slope = run Δ ( ) Given 2 points Slope = 2 2 In an equation 1 1 1) = 2 7 2) (-2, 3) ( 3, -1) 3) table ) = 7 6) = 5 7) 8) 4) 5 = ½ ( 4) Slope = the number net to. (Ma need to convert the equation so that it is in intercept form: = m + b) Which s are parallel? Which s are perpendicular? 9) (-1, 5) (0, 4) 10) = ) 2 = ) = 5 Notes on horizontal and vertical lines: Horizontal lines have. Vertical lines have. 13) = - ¼ ) (0, 4) (3, 4) 15) 16) To find the equation of a horizontal line, see where it crosses the - ais (call it "b"). The equation is. To find the equation of a vertical line, see where it crosses the - ais (call it "a"). The equation is. Which s are parallel? Which s are perpendicular?

2 Name: Linear Equations Guided Practice ~Transforming Date: Period: ~Identifing parallel and perpendicular lines from their equations 1. Describe in words how to transform the linear 2. Perform the transformation described in bo #1. equation (in the center) written in standard form to isolate the -term. 3. Describe what operation is effecting the -term. Describe what inverse operation would need to be used to transform the equation from #2 to a linear equation in intercept-form = 4 4. Perform the transformation described in #3 so that the given equation is now written in intercept form. Transforming a linear equation into -intercept form ( = m + b ) makes it eas to see what is the (m) of the line. What is the of the line above (12 4 = 4 )? Given the linear equations written in standard form, transform each equation to intercept form. a = 12 b. 6 3 = 21 c = 20 d = 12 Identif which of the above equations are equations of parallel lines/perpendicular lines. Parallel lines Perpendicular lines

3 Transformations An eample of a mapping: P P' is read P maps into P' In this eample, the preimage is and the image is. An (or a rigid transformation) is where: The pre-image and the image are congruent The shape and size are the same o Size is preserved ever segment is mapped into a segment to the original segment o Shape is preserved ever angle is mapped into an angle to the original angle Find the image of A(2, 3) and C(-1, 0) under the transformation (, ) (2, 3). A' C' Does this transformation have an fied points? What is it? Translations Fill in the rows for "Translations" in the Unit Focus chart. Is it an isometr? Sliding a figure on the plane is called a. The mapping notation for a certain translation is (, ) ( + 4, 2). Find the image of (7, 2) under this translation. Describe this translation in words (right, left, up, down, etc): Give the rule (in mapping notation) of the translation that maps (4, 1) into (-3, 2). Also, describe this translation in words: How are the s of segments affected under a translation? This means that the preimage segment and the image segment are. Reflections Fill in the rows for "Reflections" in the Unit Focus chart. Is it an isometr? Flipping a figure on the plane is called a. This is related to the idea of smmetr. Find the image of (3, 1) under the following reflections: Across the -ais Across the -ais Across the line = 4 Across the line = -1.5 Across the line = Across the line = - The mapping for a particular reflection is (, ) (, -). Is this a reflection in the -ais or -ais? Under this reflection, the preimage of (3, -7) is. the segment with endpoints E(-3, 3) and F(3, 1). Find the equation of the line EF. How would the be affected under a reflection in the -ais? How would the -intercept be affected under a reflection in the -ais? How would the -intercept be affected under a reflection in the -ais? For ever reflection, what is the line of smmetr? Where are the fied points? How is the distance from the preimage to the line of reflection, related to the distance from the image to the line of reflection?

4 More on Reflections Name: Date: Points, lines and figures can be reflected over lines other than the -ais and -ais on the coordinate plane. If we reflect P(1,6) over the line = -2, the image will be P (-5,6). Plot P on the graph. What is the distance from P to the line = -2? P What is the distance from P to the line = -2? What is the of = -2? What is the of PP '? Now reflect S(1,6) over the line = 3. What are the coordinates of S? What is the distance from S to the line = 3? What is the distance from S to the line = 3? What is the of = 3? SS '? What is the of Using this information, what conjectures can ou make about reflections over lines? We can phsicall transform points, lines and figures over an line if we remember two important concepts about reflections. all corresponding pre-image and image points must be equidistant from the line of reflection. for an point P on the preimage, and corresponding point P on the image, PP ' must be perpendicular to the line of reflection. Let s consider two other important lines of the coordinate plane, = and = -. On the grid, graph the line =. Plot A(3,7). Draw a line perpendicular to = that contains A. Calculate the distance from A to the line =. Using this distance, determine the coordinates of point A if A is reflected over the line =. Repeat the process for B(-4,-2). The distance from B to the line = is and the coordinates of B are. Describe this transformation in mapping notation. Now, graph the line = -. Plot A(3,7). Draw a line perpendicular to = - that contains A. Calculate the distance from A to the line = -. Using this distance, determine the coordinates of point A if A is reflected over the line = -. Repeat the process for B(-4,-2). The distance from B to the line = - is and the coordinates of B are. Describe this transformation in mapping notation. From Algebra I, ou ma remember that = is the parent of all linear functions. In future math studies, ou will learn that all transformations of lines can be described algebraicall from this one parent equation.

5 Linear Equations Windowpane # 1 Geometr tetbook 3-6, pg 165 (), pg 172 (calculator) Name: Date: _ Period: Parallel & Perpendicular lines have the SAME. lines have OPPOSITE RECIPROCAL s. Point-Slope Form 1 = m( 1 ) Distribute and solve for m = rise run ( ) ( Δ) -intercept Δ = Table or points on the line STAT, Edit, input in L1 and in L2, STAT, Calc, LinReg, ENTER A + B = C = m + b (0, b) (No fractions, and is positive.) Solve for If necessar, multipl b the denominator to get rid of a fraction. Then add/subtract to bring and to the same side. where the line crosses the -ais Use the given information to fill in the windowpane. Show our work and circle our answers. 1. Write the equation of a line with -intercept of 5 and a of ¾. Put our equation in standard form. Parallel and Perpendicular Point-Slope Form = = -intercept 2. Write the equation of a line with -intercept of 3 and a of 5. Parallel and Perpendicular Point-Slope Form = = -intercept

6 3. Write the equation of a line containing the points (2, 1) and (3, 4). Parallel and Perpendicular Point-Slope Form = = -intercept 4. 2 = 5 Parallel and Perpendicular Point-Slope Form = = -intercept 5. Write the equation of a line 9 units above and parallel to the -ais. Parallel and Perpendicular Point-Slope Form = = Horizontal line has. Vertical line has. -intercept For a review on, see pg 165. For a review on using graphs and tables on the graphing calculator, see pg 172. The eamples in the tetbook sections 3-6 and 3-7 are good, as well as the powerpoint notes on

7 Scavenger Hunt: PDM and PLP SHOW YOUR WORK!! Name: Date: _ Period: Station Letter: Diagram: ANSWER Station Letter: Diagram: ANSWER Concept/theorem/formula: Calculations/Reasoning: Concept/theorem/formula: Calculations/Reasoning: Station Letter: Diagram: ANSWER Station Letter: Diagram: ANSWER Concept/theorem/formula: Calculations/Reasoning: Concept/theorem/formula: Calculations/Reasoning:

8 Pthagorean Theorem, Distance, Midpoint (PDM) PDM-1. Circle Q has a diameter WY. Point W is located at (3, -2) and point Y is located at (-5, -6). What are coordinates of Q, the center of the circle? What is the length of the radius of the circle? PDM-2: Mrs. Cheung hired a landscaping service to plant a row of bushes around her triangular backard. PDM-3: A wooden pole was broken during a wind-storm. Before it broke, the total height of the pole above the ground was 25 feet. After it broke, the top of the pole touched the ground 15 feet from the base. How tall was the part of the pole that was left standing? If the bushes must be planted 3 feet apart, approimatel how man bushes are needed for Mrs. Cheung s backard? PDM-8: There is a building with a 12 ft high window. You want to use a ladder to go up to the window, and ou decide to keep the ladder 5 ft awa from the building to have a good slant. How long should the ladder be? PDM-10: An equilateral triangle has vertices at (0,0) and (6,0) in a coordinate plane. What are the coordinates of the third verte? You ma want to sketch it out. PDM-9: On a baseball diamond the bases are 90 ft apart. What is the distance from home plate to second base in a straight line? PDM-11: Find out the length of sides a and b on the following triangle: Note: The sides of an equilateral triangle are identical in length. PDM-12: Look at the following figure. Start b finding the value for X 1, then for X 2, then X 3, and so on until ou get the value for X 6. Write the lengths as square roots, as that makes it simpler. What is the value of X 6? PDM-13: We have a wooden bo that measures 4 ft. b 3 ft. b 2 ft.: Points, Lines, Planes (PLP) What is the longest straight pole, like the red one, that ou can have inside the bo? PLP-2. The following problem was assigned for homework: F is between E and G. EG = 100, EF = 4 20, FG = Mar and John make these conclusions: Mar: F is the midpoint of EG. John: F is not the midpoint of EG. Who is correct Mar, John, or neither? Eplain wh. PLP-8. Given: Two angles are complementar. The measure of one angle is 20 more than the measure of the other angle. Conclusion: The measures of the angles are 40 and 60. Is this conclusion valid or invalid? Eplain our reasoning.