Question

Iliana rotated trapezoid WXYZ 180° about the origin.

On a coordinate plane, trapezoid W X Y Z has points (negative 4, 2), (negative 3, 4), (negative 1, 4), (0, 2).

What is the correct set of image points for trapezoid W’X’Y’Z’?

W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
W’(4, 2), X’(3, 4), Y’(1, 4), Z’(0, 2)
W’(–2, –4), X’(–4, –3), Y’(–4, –1), Z’(–2, 0)
W’(2, 4), X’(4, 3), Y’(4, 1), Z’(2, 0)

Answer 1

To find the image points of trapezoid WXYZ after rotating it 180° about the origin, we need to apply the transformation rule for a 180° rotation about the origin. The rule is that any point (x, y) becomes (-x, -y).

Let's apply this transformation to each point of trapezoid WXYZ:

1. Point W(-4, 2):
- W' = (4, -2)

2. Point X(-3, 4):
- X' = (3, -4)

3. Point Y(-1, 4):
- Y' = (1, -4)

4. Point Z(0, 2):
- Z' = (0, -2)

Now, we can compile the image points for trapezoid W'X'Y'Z':
- W’(4, –2)
- X’(3, –4)
- Y’(1, –4)
- Z’(0, –2)

Thus, the correct set of image points for trapezoid W’X’Y’Z’ is:

**W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)**.