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Question 11 (2 points)
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(Rotations MC)
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)
OU'(-1, 0), V'(-3, 0), W'(3,-3)
estion 12 (2 points)

Verified Answer :

GinnyAnswer

To determine the vertices of the image \(\(U'V'W'\)\) after rotating triangle \(\(UVW\)\) 180° counterclockwise, we need to apply the rotation transformation to each vertex of the triangle.

A rotation by 180° counterclockwise (which is the same as a 180° clockwise rotation due to symmetry) about the origin can be achieved using the following transformation:
\(\[ (x', y') = (-x, -y) \]\)

This means for any vertex \(\((x, y)\)\), the new coordinates after the rotation will be \(\((-x, -y)\)\).

Let's apply this transformation to each vertex of triangle \(\(UVW\)\):

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

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

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

So, the vertices of the image \(\(U'V'W'\)\) after rotating 180° counterclockwise are:
\(\[ U'(2, 0), V'(3, -1), W'(3, -3) \]\)

Therefore, the correct answer is:
\(\[ \boxed{U'(2, 0), V'(3, -1), W'(3, -3)} \]\)

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