Drawing Shapes on a Coordinate Grid (Cartesian Plane) Paper, pencils, extra worksheets, centimetre paper


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1 Mini Lesson Topic Drawing Shapes on a Coordinate Grid (Cartesian Plane) Paper, pencils, extra worksheets, centimetre paper Show them exactly how to do it. Watch me do it, or Let s take a look at how (individual, text) Today we are going to be using ordered pairs to describe the position of a shape on a coordinate grid or cartesian plane. Let s take a look at how Aria does this. Aria is designing a rectangular playground for a local park in Victoria. To help plan the playground, Aria drew a rectangle on a coordinate grid. She used the scale 1 square represents 2m. To describe the rectangle, we label its vertices with letters. The letters are written in order as you move around the perimeter of the shape. We then use coordinates to describe the locations of the vertices. Point A has coordinates (4, 6) Point B has coordinates (4, 18) Point C has coordinates (20, 18) Point D has coordinates (20, 6) With a partner, try and use a coordinate grid to help find the length and width of the playground. Strategy #1  Counting Squares There are 8 squares along the horizontal segment AD. The side length of each square represents 2 m. So, the playground has length: 8 x 2 m = 16 m There are 6 squares along the vertical segment AB. The side length of each square represents 2 m. So, the playground has width: 6 x 2 m = 12 m
2 Strategy #2  Using the Coordinates Jarrod used the coordinates of the points. The first coordinate of an ordered pair tells how far you move right. The horizontal distance between D and A is: 204 = 16 So, the playground has length 16 m. The second coordinate of an ordered pair tells how far you move up. The vertical distance between B and A is: 186 = 12 So, the playground has width 12 m. Draw and label a coordinate grid. a) Plot each point on the grid. What scale will you use? Explain your choice. J (4, 2) K (4, 10) L (10, 12) M (10, 4) b) Join the points in order. Then describe the shape you have drawn. In the future, when describing a shape, you can use a coordinate grid (or cartesian plane) to be specific and accurate in your descriptions of position, length, widths, etc. How do you decide which scale to use when plotting a set of points on a grid? Is more than one scale sometimes possible? Explain. Mini Lesson Topic Show them exactly how to do it. Watch me do it, or Let s take a look at how (individual, text) Transformations on a Coordinate Grid  Translations Paper, pencils, extra worksheets, centimetre paper, onion paper We have already learned how to describe the position of a shape on a coordinate grid. Now we are going to transform the positions of these shapes. We will still use the cartesian plane to accurately describe the beginning and end positions of the shapes. If possible, watch Pearson Animation Video. Let s examine the following example: Triangle ABC was translated 5 squares right and 2 squares down. It s translation image is triangle A B C.
3 Each vertex moved 5 squares right and 2 squares down to its image position. After a translation, a shape and its image face the same way. The shape and its image are congruent. That is, corresponding sides and corresponding angles are equal. We can show this by measuring. With a partner, try and answer the following question: Copy this triangle on a grid: D (6, 10) E (10, 7) (7, 6) a) Draw the image of triangle DEF after the translation 6 squares left and 1 square down. b) Write the coordinates of the vertices of the image triangle. How are the coordinates related to the coordinates of the vertices of the prime triangle? Another point on this grid is G (10, 2). Using the translation above (6 squares left and 1 square down), predict the coordinates of point G after the same translation. Translations are only one type of transformation that shapes can undergo. Mini Lesson Topic Show them exactly how to do it. Watch me do it, or Let s take a look at how (individual, text) Transformations on a Coordinate Grid  Reflections Paper, pencils, extra worksheets, centimetre paper, onion paper We have already learned how to describe the position of a shape on a coordinate grid. Now we are going to transform the positions of these shapes. We will still use the cartesian plane to accurately describe the beginning and end positions of the shapes. If possible, watch Pearson Animation Video. Let s examine the following example: Quadrilateral JKLM was reflected in a vertical line through the horizontal axis at 5. Its reflection image is Quadrilateral J K L M.
4 Each vertex moved horizontally so the distance between the vertex and the line of reflection is equal to the distance between its image and the line of reflection. After a reflection, a shape and its image face opposite ways. The shape and its image are congruent. We can show this by tracing the shape, then flipping the tracing. The tracing and its image match exactly. With a partner, try and answer the following question: Copy this triangle on a grid: S (2, 9) T (5, 7) U (8, 10) a) Draw the image of triangle STU after a reflection in the line of reflection. b) Write the coordinates of the vertices of the image triangle. Describe how the positions of the vertices have changed from the vertices of the prime triangle. Another point on this grid is V (4, 3). Predict the location of point V after a reflection in the same line. How did you make your prediction? Translations and reflections are only two types of transformations that shapes can undergo. Mini Lesson Topic Transformations on a Coordinate Grid  Rotations Paper, pencils, extra worksheets, centimetre paper, onion paper We have already learned how to describe the position of a shape on a coordinate grid. Now we are going to transform the positions of these shapes. We will still use the cartesian plane to accurately describe the beginning and end positions of the shapes.
5 Show them exactly how to do it. Watch me do it, or Let s take a look at how (individual, text) If possible, watch Pearson Animation Video. Let s examine the following example: When a shape is turned about a point, it is rotated. A complete turn measures 360. So we can name fractions of turns in degrees. A 1/4 turn in a 90 rotation. A 1/2 turn is a 180 rotation. A 3/4 turn is a 270 rotation. Trapezoid PQRS was rotated a 3/4 turn clockwise about vertex R. Its rotation image is Trapezoid P Q R S. The sides and their images are related. For example, The distances of S and S from the point of rotation, R, are equal; that is, SR = RS Reflex angle SRS = 270, which is the angle of rotation. After a rotation, a shape and its image may face different ways. Since we trace the shape and use the tracing to get the image,
6 the shape and its image and its image are congruent. With a partner, try and answer the following question: Copy this quadrilateral on a coordinate grid. A (4, 2) B (3, 4) C (4, 7) D (6, 3) Trace the quadrilateral on tracing paper. a) Draw the image of the quadrilateral after a rotation of 90 clockwise about vertex B. b) Write the coordinates of the vertices. Using the same quadrilateral. a) Draw the image of the quadrilateral after a rotation of 270 clockwise about vertex B. b) Draw the image of the quadrilateral after a rotation of 270 counterclockwise about vertex B. Translations, reflections, and rotations are some of the transformations that shapes can undergo. How does a coordinate grid help you describe a transformation of a shape?
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