Lesson 3
Making the Moves
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=20240727T002035Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=37faf5277093dbcbf88bab554d2623fccd0d1c184fd60eb174665c17c0ba5463)
- A translation which takes \(P\) to \(P’\)
- A counterclockwise rotation of A, using center \(P\), of 60 degrees
- A reflection of A across line \(\ell\)
Solution
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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=20240727T002035Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b23e5b4135b45a78f92da10e6c985060003808bbbbfbbdecf82d5fb13ad1bc6d)
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.
Solution
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Problem 3
Here is quadrilateral \(ABCD\) and line \(\ell\).
![Quadrilateral \(A \) \(B\) \(C\) \(D\) and dashed line \(l\) with a positive slope. \(B\) \(C\) is parallel to line \(l\).](https://cms-im.s3.amazonaws.com/w69G4VaZ4wDGKq6Tb8dqthc2?response-content-disposition=inline%3B%20filename%3D%228-8.1.A2.newPP.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A2.newPP.04.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=20240727T002035Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9489a49ca98c6f5cddd09cf5ba9839ab47e3ea62b59c2f63bbbe2268598c5fcc)
Draw the image of quadrilateral \(ABCD\) after reflecting it across line \(\ell\).
Solution
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(From Unit 1, Lesson 2.)