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° 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′(−2, 0), V′(−3, 0), W′(3, −3)
To determine the vertices of the image after rotating 90° counterclockwise, we can use the following rotation formula:
x' = -y
y' = x
Let's apply this formula to each vertex of the preimage:
For U(-2, 0):
x' = 0
y' = 2
U' = (0, 2)
For V(-3, 1):
x' = -1
y' = -3
V' = (-1, -3)
For W(-3, 3):
x' = -3
y' = -3
W' = (-3, -3)
Therefore, the vertices of the image U'V'W' after rotating 90° counterclockwise are U'(0, 2), V'(-1, -3), W'(-3, -3). So, the correct answer is U′(0, 2), V′(−1, −3), W′(−3, −3).