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