# Lesson 5

Describing Transformations

Let’s transform some polygons in the coordinate plane.

### Problem 1

Here is Trapezoid A in the coordinate plane:

- 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.

### Problem 4

Here is quadrilateral \(ABCD\).

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.