Key Ideas/ Vocabulary

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1 Name: Date: Unit 1 oordinates and Design 1.1 The artesian Plane Key Ideas/ Vocabulary P , 13-15, reate Designs P , 9-12 Math 7 hapter 1 1 P a g e

2 1.3 Transformations P , Horizontal and Vertical Distances P , 13, 14 hapter Review P 36 Practice Test P 38 Math 7 hapter 1 2 P a g e

3 1.1 The artesian Plane Where do we see grids in real life? lueprints and maps Parts of a coordinate grid y - axis y-axis II I + 3 x-axis origin origin x - axis (0, 0) - 4 quadrants III IV What are the signs of the x-coordinates and y-coordinates for the following quadrants? x y x y Quadrant 1 (+, +) Quadrant 2 (-, +) x y x y Quadrant 3 (-, -) Quadrant 4 (+, -) Math 7 hapter 1 3 P a g e

Example 1: Identify Points on a oordinate Grid Starting at the origin go to the right 9 units. Then go down 2 units. So the coordinates for is 9 units to the right of the origin.

4 Example 1: Identify Points on a oordinate Grid Starting at the origin go to the right 9 units. Then go down 2 units. So the coordinates for is 9 units to the right of the origin. So, the x-coordinate is 9. Point is 2 units down from the origin. So the y-coordinate is -2. Point has the coordinates (9, -2) Using this method find the coordinates for the rest of the points. Point oordinates 9 units to the right of the origin and 2 units down. (9, 2) 7 units to the right of the origin and 5 units down. (7, -5) 2 units to the right of the origin and 4 units down. (2, -4) D 2 units to the right of the origin and 1 unit down. (2, -1) E 0 units from the origin and 1 unit up. (0, 1) F 2 units to the left and 3 units up. (-2, 3) G 7 units to the left and 4 units up. (-7, +4) Math 7 hapter 1 4 P a g e

5 Example Plot Points on a oordinate Grid Plot the following points to form a constellation: (-10, 9), (-5, 5), (0, 2), D(3, -2), E(-5, -3), F(3, 7). 9 units up 10 units to the left E F D Point oordinates (-10,9) 10 units to the left and 9 units up. (-5, 5) 5 units to the left and 5 units up. (0, 2) 0 units to the left or right and 2 units up. D (3, -2) 3 units to the right and 2 units down. E (-5, -3) 5 units to the left and 3 units down. F (3, 7) 3 units to the right and 7 units up. Math 7 hapter 1 5 P a g e

reate Designs Many designs can be draw using a coordinate grid. ould these flags been created using a coordinate grid? How do you draw a design on a coordinate grid? 1.

6 reate Designs Many designs can be draw using a coordinate grid. ould these flags been created using a coordinate grid? How do you draw a design on a coordinate grid? 1. Draw a coordinate grid on grid paper. Label the axes by 5s from 10 to Plot the following points: ( 10, 10), (10, 10), (10, 10), and D( 10, 10). onnect them in alphabetical order from to D. onnect D to. 3. On the same piece of grid paper, plot these points: E(2, 5), F(2, 2), G(5, 2), H(5, 2), I(2, 2), J(2, 5), K( 2, 5), L( 2, 2), M( 5, 2), N( 5, 2), P( 2, 2), and Q( 2, 5). onnect the points in alphabetical order from E to Q. onnect Q to E. olour the inside of this design red. D N G I -2 M L H -3 Q P K Math 7 hapter 1 6 P a g e E F J G

Reflect on Your Findings 4. a) What does the flag you created look like? Switzerland Flag b) Do you think you would have drawn the same design if you had connected the points in a different order?

Example 1: Identify the oordinates of Vertices Identify the coordinates of the vertices of the shape. Vertices are the points where two lines meet. Label each vertex.

7 Reflect on Your Findings 4. a) What does the flag you created look like? Switzerland Flag b) Do you think you would have drawn the same design if you had connected the points in a different order? Explain. Yes, if we connected them in the backward order. No if we used random connections, since you d have different sides. Example 1: Identify the oordinates of Vertices Identify the coordinates of the vertices of the shape. Vertices are the points where two lines meet. Label each vertex. D Example 2: Draw a Design Draw the flag of the zech Republic on a coordinate grid E D F Use this coordinate grid to place all of the vertices of the design where you think they belong on the coordinate grid. Label all the vertices and write their coordinates using ordered pairs: (1, -1), (10, -1), (10, -4), D(5,-7), E(1, -7), F(10, -7). onnect through D. onnect D to E and E to F and color it red. onnect to E and color the triangle blue. Math 7 hapter 1 7 P a g e

8 1.2 Transformations What is a transformation? transformation is when a geometric figure is moved. How do you describe a translation? translation is when you slide an object along a straight line. Slide Δ 6 units to the right and two units up. Label the new triangle units to the right. 2 units up How do you describe a reflection? reflection is a mirror image. The mirror line is called a line of reflection. Flip the triangle over the y-axis. Label the new triangle '. Line of reflection ompare the distance of and from the line of reflection. and are the same distance from the line of reflection, 1 unit. ompare the distance of and from the line of reflection. and are the same distance from the line of reflection,5 units. -2 Predict the distance of and from the line of reflection. and are the same distance from the line of reflection, 4 units. Math 7 hapter 1 8 P a g e

9 How do you describe rotation? rotation is a turnabout a fixed point called the centre of rotation. Rotate the trapezoid D about 90 clockwise. Label the new trapezoid ```D`. D D D E Math 7 hapter 1 9 P a g e

10 G F H E N T E R Math 7 hapter 1 10 P a g e

Vertical distance is along the y-axis and is 5 units up. 1.3 Horizontal and Vertical Distances How do you describe horizontal and vertical movement? 1. You can describe movement by playing a game on a grid.

11 Vertical distance is along the y-axis and is 5 units up. 1.3 Horizontal and Vertical Distances How do you describe horizontal and vertical movement? 1. You can describe movement by playing a game on a grid. The object of this game is to get the baseball in the glove. You can move the ball using only rotations, reflections, and translations. a. Rotate the ball 180 clockwise around the centre of rotation. What is the ball s new position? (4, 2) b. Translate the ball from the position after rotation to the glove. How would you describe this translation? Horizontal distance is along the x- axis and is 9 units to the right. The ball must move 1 unit to the right and 1 unit up to the glove after the rotation. c. How many transformations did it take to put the ball in the glove? It took two transforamtion to put the ball in the glove. (Rotation and translation.) Describe the total horizontal and vertical distance the ball travelled from start to finish. The ball travelled 9 units horizontally right, and 5 units vertically up. Math 7 hapter 1 11 P a g e

1. Rotate the ball about 90 counterclockwise.

The ball moved 11 horizontal units to the

12 1. Rotate the ball about 90 counterclockwise. 2. Reflect the ball along the y-axis. 3. Translate the ball 2 units to the right and 1 unit down. The ball moved 11 horizontal units to the left and 6 vertical units down. YOU TRY! Find another path. Math 7 hapter 1 12 P a g e

13 Example 2: Describe the Movement of the Vertices of a Shape a. Reflect this shape in the x-axis. Then, translate it 4 units horizontally left and 2 units vertically up. b. What are the coordinates of vertex and vertex? c. Describe the movement of vertex to vertex and vertex to vertex Translation 4 units horizontally left and 2 units vertically up. (-2, 4) (1, 7) +4 Reflection along the x-axis. +2 (2, 2) (5, 5) Vertex moved 4 units horizontally left and 6 units vertically up. Vertex moved 4 units horizontally left and 12 units vertically up. Math 7 hapter 1 13 P a g e

Drawing Shapes on a Coordinate Grid

Drawing Shapes on a Coordinate Grid UNIT STUDENT OOK LESSO N Drawing Shapes on a oordinate Grid Quick Review t t Home Sc h o o l To describe the position of a shape on a grid, we use ordered pairs. The numbers in an ordered pair are called