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