Lesson 3
Making the Moves
Let's draw and describe translations, rotations, and reflections.
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T150850Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1d7ee9968849fc80f0ac66cf17fd997479663e0bb76ddc0619d212516f5644d1)
- 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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T150850Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=eae21cd03fa711876b9ab6a31fc092a3bb5e558720563ba5c060dec1af30df4d)
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
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T150850Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=334b225d2b7e30a63ff6fdd8fc3e40648b5898fe0dfbeb6994240979381fb309)
Draw the image of quadrilateral \(ABCD\) after reflecting it across line \(\ell\).