Question

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 180° counterclockwise.

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′(−1, 0), V′(−3, 0), W′(3, −3)

Answer 1

To determine the vertices of image U′V′W′ after a 180° counterclockwise rotation, we can apply the following transformation rules:

• A 180° counterclockwise rotation of a point (x, y) about the origin produces the point (-x, -y).
• To perform a rotation of a polygon, we apply the transformation rule to each vertex of the polygon.

Using these rules, we can find the vertices of image U′V′W′ as follows:

• Vertex U(-2, 0) is transformed to U′(0, -2), since (-(-2), -(0)) = (2, 0) becomes (0, -2) after the rotation.
• Vertex V(-3, 1) is transformed to V′(1, -3), since (-(-3), -(1)) = (3, -1) becomes (1, -3) after the rotation.
• Vertex W(-3, 3) is transformed to W′(3, -3), since (-(-3), -(3)) = (3, 3) becomes (3, -3) after the rotation.

Therefore, the vertices of image U′V′W′ after a 180° counterclockwise rotation are U′(0, -2), V′(1, -3), and W′(3, -3).

So, the answer is option (b) U′(0, −2), V′(1, −3), W′(3, −3).