Triangle UVW has vertices at U(−2, 0), V(−3, 1), W(−3, 3). Determine the vertices of image U′V′W′ if the preimage is rotated 90° clockwise.

Question

U′(0, −2), V′(−1, −3), W′(−3, −3)
U′(0, 2), V′(1, 3), W′(3, 3)
U′(2, 0), V′(3, −1), W′(3, −3)
U′(−2, 0), V′(−3, 1), W′(3, −3)

Answer 1

To rotate a point \((x, y)\) 90° clockwise around the origin, we use the transformation:

\[ (x, y) \rightarrow (y, -x) \]

Let's apply this transformation to each of the vertices of triangle UVW.

1. For point \(U(-2, 0)\): \[ U' = (0, -(-2)) = (0, 2) \]

2. For point \(V(-3, 1)\): \[ V' = (1, -(-3)) = (1, 3) \]

3. For point \(W(-3, 3)\): \[ W' = (3, -(-3)) = (3, -3) \]

Now we have the transformed coordinates of the vertices:

• \(U' = (0, 2)\)
• \(V' = (1, 3)\)
• \(W' = (3, -3)\)

Comparing with the given options, the coordinates \(U'(0, 2)\), \(V'(1, 3)\), and \(W'(3, -3)\) match:

U′(0, 2), V′(1, 3), W′(3, −3)

Thus, the answer is:

U′(0, 2), V′(1, 3), W′(3, −3)