Question

Triangle LMN is drawn with vertices at L(−2, 1), M(2, 1), N(−2, 3). Determine the image vertices of L′M′N′ if the preimage is rotated 90° clockwise.

L′(1, 2), M′(1, −2), N′(3, 2)
L′(−1, 2), M′(−1, −2), N′(−3, 2)
L′(−1, −2), M′(−1, 2), N′(−3, −2)
L′(2, −1), M′(−2, −1), N′(2, −3)

Answer 1

To determine the image vertices \( L', M', N' \) of triangle \( LMN \) when rotated 90° clockwise, we need to apply the rotation transformation to each vertex.

The rule for rotating a point \( (x, y) \) 90° clockwise about the origin is given by the transformation:

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

Now, applying this transformation to each vertex of triangle \( LMN \):

1. **Vertex L (-2, 1)**:
\[
L' = (1, -(-2)) = (1, 2)
\]

2. **Vertex M (2, 1)**:
\[
M' = (1, -2) = (1, -2)
\]

3. **Vertex N (-2, 3)**:
\[
N' = (3, -(-2)) = (3, -2)
\]

Now we have the transformed vertices:
- \( L' = (1, 2) \)
- \( M' = (1, -2) \)
- \( N' = (3, 2) \)

Comparing these results with the provided options:
- **L' (1, 2)**, **M' (1, -2)**, **N' (3, 2)**

We see that this corresponds to the first option:
\[
L'(1, 2), M'(1, -2), N'(3, 2)
\]

Thus, the correct answer is:

**L′(1, 2), M′(1, −2), N′(3, 2)**.