Question

collaborative activity: what does it do? quadrilateral abcd is shown on the coordinate plane. 1. apply each rule to quadrilateral abcd, and graph the resulting image. label the image with the letter indicated, and then describe the transformation. a. figure qq (x,y)→( - x, - y) move the red dot below and place it on the coordinate plane to show your answer. b. figure r: (x,y)→( - y, - x) move the blue dot below and place it on the coordinate plane to show your answer. c. figure s: (x,y)→(y, - x) move the yellow dot below and place it on the coordinate plane to show your answer. points: 3 points

Explanation:

Step1: Analyze transformation for Figure QQ

The rule $(x,y)\to(-x, -y)$ is a rotation of $180^{\circ}$ about the origin. For each vertex of quadrilateral $ABCD$ with coordinates $(x,y)$, we change the sign of both the $x$ - coordinate and the $y$ - coordinate.

Step2: Analyze transformation for Figure R

The rule $(x,y)\to(-y,-x)$ is a rotation of $270^{\circ}$ counter - clockwise (or $90^{\circ}$ clockwise) about the origin. We swap the $x$ and $y$ coordinates and change their signs.

Step3: Analyze transformation for Figure S

The rule $(x,y)\to(y,-x)$ is a rotation of $90^{\circ}$ counter - clockwise about the origin. We swap the $x$ and $y$ coordinates and change the sign of the new $x$ (original $y$) coordinate.

Answer:

a. Rotation of $180^{\circ}$ about the origin.
b. Rotation of $270^{\circ}$ counter - clockwise (or $90^{\circ}$ clockwise) about the origin.
c. Rotation of $90^{\circ}$ counter - clockwise about the origin.