Question

Polygon KLMN is drawn with vertices at K(1, 5), L(1, 0), M(−1, −1), N(−4, 2). Determine the image vertices of N′ if the preimage is rotated 90° counterclockwise.

N′(−4, 2)
N′(4, −2)
N′(−2, −4)
N′(2, 4)

Answer 1

To find the image of point N(−4, 2) after a 90° counterclockwise rotation about the origin, we can use the rotation formula for points:

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

Given the coordinates of point N(−4, 2):

- \(x = -4\)
- \(y = 2\)

Applying the rotation formula:

- \(x' = -y = -2\)
- \(y' = x = -4\)

Thus, the coordinates of N′ after the 90° counterclockwise rotation are:

\[
N′(−2, −4)
\]

So, the correct choice from your options is:

**N′(−2, −4)**.