Question

Which shows the pre-image of quadrilateral W'X'Y'Z' before the figure was rotated according to the rule (x, y) → (–x, –y)?

On a coordinate plane, a quadrilateral has points W prime (2, 3), X prime (6, 3), Y prime (6, 4), Z prime (3, 5).

On a coordinate plane, a quadrilateral has points W (negative 3, 2), X (negative 3, 6), Y (negative 4, 6), Z (negative 5, 3).
On a coordinate plane, a quadrilateral has points W (3, negative 2), X (3, negative 6), Y (4, negative 6), Z (5, negative 3).
On a coordinate plane, a quadrilateral has points W (negative 2, negative 3), X (negative 6, negative 3), Y (negative 6, negative 4), Z (negative 3, negative 5).
On a coordinate plane, a quadrilateral has points W (negative 3, negative 2), X (negative 3, negative 6), Y (negative 4, negative 6), Z (negative 5, negative 3).

Answer 1

To find the pre-image of the quadrilateral W'X'Y'Z' before it was rotated according to the rule \((x, y) \rightarrow (-x, -y)\), we need to apply the inverse action of the transformation to each point of the quadrilateral W'X'Y'Z'.

Given the points of W'X'Y'Z':
- \(W' = (2, 3)\)
- \(X' = (6, 3)\)
- \(Y' = (6, 4)\)
- \(Z' = (3, 5)\)

To find the pre-image points, we take each coordinate of W', X', Y', and Z' and apply the reverse transformation, which for the given rule means replacing \((x, y)\) with \((-x, -y)\):

1. \(W = (-2, -3)\)
2. \(X = (-6, -3)\)
3. \(Y = (-6, -4)\)
4. \(Z = (-3, -5)\)

Now we need to match these points with the given options.

Looking through the options, the matching pre-image is:
- W: (-2, -3)
- X: (-6, -3)
- Y: (-6, -4)
- Z: (-3, -5)

This corresponds to the fourth option:
- **On a coordinate plane, a quadrilateral has points W (negative 2, negative 3), X (negative 6, negative 3), Y (negative 6, negative 4), Z (negative 3, negative 5).**

Thus, the correct answer is:
**On a coordinate plane, a quadrilateral has points W (negative 2, negative 3), X (negative 6, negative 3), Y (negative 6, negative 4), Z (negative 3, negative 5).**