Question

quadrilateral WVUT undergoes a counterclockwise rotation of 90 degrees.
W(-4,1), V(-5,-4), U(-3,0), and T(0,-1)
What are the coordinates of the image W'V'U'T'?

Answer 1

To find the coordinates of the image of quadrilateral WVUT after a counterclockwise rotation of 90 degrees, we will apply the rotation transformation to each vertex.

The general rule for rotating a point \((x, y)\) counterclockwise by 90 degrees about the origin is:
\[
(x, y) \to (-y, x)
\]

Now we will apply this transformation to each vertex:

1. **Point W**:
\[
W(-4, 1) \to W'(-1, -4)
\]

2. **Point V**:
\[
V(-5, -4) \to V'(4, -5)
\]

3. **Point U**:
\[
U(-3, 0) \to U'(0, -3)
\]

4. **Point T**:
\[
T(0, -1) \to T'(1, 0)
\]

Now, let's summarize the new coordinates of the vertices \(W', V', U', T'\):

- \(W'(-1, -4)\)
- \(V'(4, -5)\)
- \(U'(0, -3)\)
- \(T'(1, 0)\)

Thus, the coordinates of the image \(W'V'U'T'\) after a counterclockwise rotation of 90 degrees are:

- \(W'(-1, -4)\)
- \(V'(4, -5)\)
- \(U'(0, -3)\)
- \(T'(1, 0)\)