Let's start by plotting the given vertices W(- 5,0), X(- 1,4), Y(3,- 1), and Z(0,-4). Then we will connect them with line segments to draw the quadrilateral.
We want to rotate the image of WXYZ by 270^(∘) counterclockwise about vertex W. A rotation by 270^(∘) counterclockwise ends up in the same place as a rotation by 90^(∘) clockwise. Therefore, we can use a protractor to draw a ray that makes a 90^(∘) angle with WZ at W. For simplicity, let's start by rotating only one point. We will use vertex Z.
On this ray, we will mark a point Z' that is the same length as WZ. This is the image of Z after the rotation.
Next, we will repeat the same process for vertices X and Y to obtain X' and Y'. Since W is the point at which the quadrilateral is rotated, W' will be in the same position as W. The coordinates of the images of the vertices are W'(- 5,0), X'(-1,- 4), Y'(- 6,- 8), and Z'(- 9, - 5).
Finally, we will connect W', X', Y', and Z' to obtain the image of WXYZ.
Extra
Visualizing the Rotation
Let's rotate WXYZ 270^(∘) counterclockwise about W so that we can see how it is mapped onto W'X'Y'Z'.
