Question

For exercises 21-23, use the following information

Parallelogram $DEFG$ with $D\left(2,4\right),E\left(5,4\right),F\left(4,1\right),\text{and}G\left(1,1\right)$ is rotated $270°$ counter clockwise about the origin.

23. Graph the pre-image and the image.

Short answer

Graph of pre-image and image is

Step-by-step solution

- Meaning of pre-image

Pre-image is the parallelogram in original position

Vertices of parallelogram $DEFG$are $D\left(2,4\right),E\left(5,4\right),F\left(4,1\right)\text{, and}G\left(1,1\right)$

- Meaning of image

Image is the parallelogram $D\text{'}E\text{'}F\text{'}G\text{'}$which is formed after rotation.

Vertices of parallelogram $D\text{'}E\text{'}F\text{'}G\text{'}$ are $D\text{'}\left(4,-2\right)\text{,}E\text{'}\left(4,-5\right)\text{,}F\text{'}\left(1,-4\right)\text{, and}G\text{'}\left(1,-1\right)$

- Plot both triangles

On Cartesian plane, plot the points of $DEFG$and join them to form a parallelogram. Then plot the points of $D\text{'}E\text{'}F\text{'}G\text{'}$ and join them to form another parallelogram.