Question

Triangle LMN is drawn with vertices at L(−4, −1), M(0, −1), N(−4, −3). Determine the image vertices of L′M′N′ if the preimage is rotated 90° clockwise.

L′(4, 1), M′(0, 1), N′(4, 3)
L′(−4, −1), M′(0, −1), N′(−4, −3)
L′(−1, 4), M′(−1, 0), N′(−3, 4)
L′(1, −4), M′(1, 0), N′(3, −4)

Answer 1

To rotate the points of triangle LMN 90° clockwise, you can use the following transformation for each point \((x, y)\):

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

Now, let's apply this transformation to each vertex of triangle LMN.

1. **For point L(−4, −1)**:
\[
L' = (-1, -(-4)) = (-1, 4)
\]

2. **For point M(0, −1)**:
\[
M' = (-1, -0) = (-1, 0)
\]

3. **For point N(−4, −3)**:
\[
N' = (-3, -(-4)) = (-3, 4)
\]

Now we have the rotated vertices:
- \(L'(-1, 4)\)
- \(M'(-1, 0)\)
- \(N'(-3, 4)\)

Comparing with the provided options, we can see that they do not exactly match, which indicates the selections provided might not contain the transformation results.

Let's reassess each option but based on our calculations, the transformed points from the calculations do not directly represent any of the listed options correctly.

Thus, the correctly calculated vertices after a 90° clockwise rotation would be:
- L'(-1, 4)
- M'(-1, 0)
- N'(-3, 4)

If you were looking for an option that fits the calculated results, none of them seem to fit accurately.