Let's start by plotting the given vertices D(- 3,- 4), E(- 5,2), F(1, - 1), and G(3,- 7). Then we will connect them with line segments to draw the quadrilateral.
We will now draw the image of DEFG after a 270^(∘) clockwise rotation about vertex E. For simplicity, let's start by rotating only one point. We will use vertex F. Notice that a rotation by 270^(∘) clockwise ends up in the same place as a rotation by 90^(∘) counterclockwise. Therefore, we can use a protractor to draw a ray that makes a 90^(∘) angle with EF at E.
On this ray, we will mark a point F' that is the same length as EF. This is the image of F after the rotation.
Next, we will repeat the same process for vertices D and G to obtain D' and G'. Since E is the point at which the quadrilateral is rotated, E' will be in the same position as E. The coordinates of the images of the vertices are D'(1,4), E'(- 5,2), F'(- 2,8), G'(4,10).
Finally, we will connect D', E', F' and G', to obtain the image of DEFG.
Extra
Visualizing the Rotation
Let's rotate DEFG 270^(∘) clockwise about the vertex E so that we can see how it is mapped onto D'E'F'G'.
