Question

Triangle LMN has vertices at L(−1, 5), M(−1, 0), N(−2, 5). Determine the vertices of image L′M′N′ if the preimage is rotated 90° counterclockwise about the origin.

L′(5, 1), M′(0, 1), N′(5, 2)
L′(−1, −5), M′(−1, 0), N′(−2, −5)
L′(−5, −1), M′(0, −1), N′(−5, −2).
L′(1, −5), M′(1, 0), N′(2, −5)

Answer 1

To rotate a point \( (x, y) \) by \( 90^\circ \) counterclockwise about the origin, the new coordinates \( (x', y') \) can be determined using the transformation:

\[
(x', y') = (-y, x)
\]

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

1. For point \( L(-1, 5) \):
\[
L' = (-5, -1)
\]

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

3. For point \( N(-2, 5) \):
\[
N' = (-5, -2)
\]

So the new vertices after the rotation are:

- \( L'(-5, -1) \)
- \( M'(0, -1) \)
- \( N'(-5, -2) \)

Thus, the correct choice from the options provided is:

**L′(−5, −1), M′(0, −1), N′(−5, −2).**