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 90° counterclockwise.

A: U′(0, −2), V′(−1, −3), W′(−3, −3)
B:U′(0, −2), V′(1, −3), W′(3, −3)
C:U′(2, 0), V′(3, −1), W′(3, −3)
D: U′(−2, 0), V′(−3, 0), W′(3, −3)

Answer 1

To find the vertices of the image after rotating 90° counterclockwise, we can use the following formula:

x' = -y
y' = x

For each vertex (x, y) in the original triangle, we can apply this formula to get the corresponding vertex in the image.

Let's start with vertex U(-2, 0):

x' = -y = 0
y' = x = -2

So, U' is at (0, -2).

Now, let's consider vertex V(-3, 1):

x' = -y = -1
y' = x = -3

So, V' is at (-1, -3).

Finally, let's consider vertex W(-3, 3):

x' = -y = -3
y' = x = 3

So, W' is at (-3, -3).

Therefore, the vertices of the image triangle U'V'W' are (0, -2), (-1, -3), and (-3, -3).

Thus, the correct answer is option A: U′(0, −2), V′(−1, −3), W′(−3, −3).