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:
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Point W: \[ W(-4, 1) \to W'(-1, -4) \]
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Point V: \[ V(-5, -4) \to V'(4, -5) \]
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Point U: \[ U(-3, 0) \to U'(0, -3) \]
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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:
- \(W'(-1, -4)\)
- \(V'(4, -5)\)
- \(U'(0, -3)\)
- \(T'(1, 0)\)