Lesson 5
Coordinate Moves
Let’s transform some figures and see what happens to the coordinates of points.
Problem 1
- Here are some points.
What are the coordinates of \(A\), \(B\), and \(C\) after a translation to the right by 4 units and up 1 unit? Plot these points on the grid, and label them \(A’\), \(B’\) and \(C’\).
- Here are some points.
What are the coordinates of \(D\), \(E\), and \(F\) after a reflection over the \(y\) axis? Plot these points on the grid, and label them \(D’\), \(E’\) and \(F’\).
- Here are some points.
What are the coordinates of \(G\), \(H\), and \(I\) after a rotation about \((0,0)\) by 90 degrees clockwise? Plot these points on the grid, and label them \(G’\), \(H’\) and \(I’\).
Problem 2
Describe a sequence of transformations that takes trapezoid A to trapezoid B.
![Quadrilateral A and its image quadrilateral B are trapezoids.](https://staging-cms-im.s3.amazonaws.com/kQ1ZXZfyTcPd7XbuacnNzX1D?response-content-disposition=inline%3B%20filename%3D%228-8.1.A4.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A4.newPP.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T160214Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=42900112b4928b1b8c08cefdde189fca4b1f60fc983ae526fbb8e7e754185b0d)
Problem 3
Reflect polygon \(P\) using line \(\ell\).
![Polygon P and dashed line \(l\) on a grid.](https://staging-cms-im.s3.amazonaws.com/bvDUYetEnp5pNr6XF7pXaa2k?response-content-disposition=inline%3B%20filename%3D%228-8.1.A3.newPP.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A3.newPP.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T160214Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=bded86f3a3ce9e16fafa100def70f70fe05a4ab6e875f9e5214f57f25dae213f)