Let's start by plotting the given vertices A(- 3,- 4), B(- 1,- 1), C(2,- 2), and D(3,- 4). Then we will connect them with line segments to draw the quadrilateral.
We will now draw the image of ABCD after a 180^(∘) counterclockwise rotation about vertex D. For simplicity, let's start by rotating only one point. We will use vertex A. To do so, we will use a protractor to draw a ray that makes a 180^(∘) angle with DA at D. Remember that a rotation by 180^(∘) ends up in the same place no matter which direction we go.
On this ray, we will mark a point A' such that DA' is the same length as DA. This is the image of A after the rotation.
Next, to obtain B' and C' we will repeat the same process for vertices B and C. Since D is the point at which the quadrilateral is rotated, D' will be in the same position as D. The coordinates of the images of the vertices are A'(9,- 4), B'(7,-7), C'(4,-6), and D'(3,- 4).
Finally, we will connect A', B', C', and D' to obtain the image of ABCD.
Extra
Visualizing the Rotation
Let's rotate ABCD 180^(∘) counterclockwise about D so that we can see how it is mapped onto A'B'C'D'.
