Lesson 3
Grid Moves
Let’s transform some figures on grids.
Problem 1
Apply each transformation described to Figure A. If you get stuck, try using tracing paper.
![A figure A with a point P, a line l and a point P prime on a triangular grid.](https://cms-im.s3.amazonaws.com/B5ZCHECcGAuoTxDw8nQ141xM?response-content-disposition=inline%3B%20filename%3D%228-8.1.A.PP.Image.0006.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A.PP.Image.0006.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T002310Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c788dd0112cc780ec1c235554a9b62d2d046e052b309f48c8b23cc3ee3425419)
- A translation which takes \(P\) to \(P’\)
- A counterclockwise rotation of A, using center \(P\), of 60 degrees
- A reflection of A across line \(\ell\)
Problem 2
Here is triangle \(ABC\) drawn on a grid.
![Triangle A B C on a grid. Let (0 comma 0) be the bottom left corner. Then the coordinates of triangle A B C are A(3 comma 8), B(5 comma 7) and C(8 comma 9).](https://cms-im.s3.amazonaws.com/num2FVR2dDJarhyRKtbMzBdo?response-content-disposition=inline%3B%20filename%3D%228-8.1.A3.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A3.newPP.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T002310Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3965f991d7c1d5b75ecd94add6421c606dcc3e92a06541c93b95ac53e156cefb)
On the grid, draw a rotation of triangle \(ABC\), a translation of triangle \(ABC\), and a reflection of triangle \(ABC\). Describe clearly how each was done.
Problem 3
- Draw the translated image of \(ABCDE\) so that vertex \(C\) moves to \(C’\). Tracing paper may be useful.
- Draw the reflected image of Pentagon \(ABCDE\) with line of reflection \(\ell\). Tracing paper may be useful.
- Draw the rotation of Pentagon \(ABCDE\) around \(C\) clockwise by an angle of 150 degrees. Tracing paper and a protractor may be useful.