Lesson 5
Describing Transformations
Let’s transform some polygons in the coordinate plane.
Problem 1
Here is Trapezoid A in the coordinate plane:
![Trapezoid \(A\) on a coordinate plane, origin \(O\) . Horizontal and vertical axis scale negative 5 to 5 by 1’s. Trapezoid \(A\) has coordinates (2 comma 1), (2 comma 3), (4 comma 4) and (4 comma 1).](https://staging-cms-im.s3.amazonaws.com/67eBQbYcNguVLYyPcdooQHdg?response-content-disposition=inline%3B%20filename%3D%228-8.1.A6.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A6.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=20240722T141815Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=662a5b442e35561a679944dbd0d0f218755d63c52b2dca532b315b746db443ab)
- Draw Polygon B, the image of A, using the \(y\)-axis as the line of reflection.
- Draw Polygon C, the image of B, using the \(x\)-axis as the line of reflection.
- Draw Polygon D, the image of C, using the \(x\)-axis as the line of reflection.
Problem 2
The point \((\text{-}4,1)\) is rotated 180 degrees counterclockwise using center \((\text{-}3,0)\). What are the coordinates of the image?
A:
\((\text{-}5,\text{-}2)\)
B:
\((\text{-}4,\text{-}1)\)
C:
\((\text{-}2,\text{-}1)\)
D:
\((4,\text{-}1)\)
Problem 3
Describe a sequence of transformations for which Triangle B is the image of Triangle A.
![Triangle A and its image triangle B on a coordinate plane, origin \(O\).](https://staging-cms-im.s3.amazonaws.com/2zGQ1PmkqXq9EqY6FSnr9Krn?response-content-disposition=inline%3B%20filename%3D%228-8.1.A6.newPP.03.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A6.newPP.03.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=20240722T141815Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b9f6207aa3fe6b17eebe4b088d1f4100b3b1bcc19ff136531d849e7a966cf7e0)
Problem 4
Here is quadrilateral \(ABCD\).
![Quadrilateral A B C D. A B, A D and D C all have negative slopes. B C has a positive slope. A B C D has no parallel sides and no right angles.](https://staging-cms-im.s3.amazonaws.com/awLCEPgA3sFPyMqxd2UeEmxz?response-content-disposition=inline%3B%20filename%3D%228-8.1.A2.newPP.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A2.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=20240722T141815Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ad5466f23e0d05fae30a89ce52adfb734c80aecbf3fe89166088c8327d6d22c2)
Draw the image of quadrilateral \(ABCD\) after each transformation.
- The translation that takes \(B\) to \(D\).
- The reflection over segment \(BC\).
- The rotation about point \(A\) by angle \(DAB\), counterclockwise.