Question

What is the coordinate for the image of point H(2, –6) under a 90° clockwise rotation about the origin?
H’(–6, –2)
H’(6, –2)
H’(–6, 2)
H’(6, 2)

Answer 1

To find the coordinates of the point \( H(2, -6) \) after a 90° clockwise rotation around the origin, we can use the following transformation rule for rotating points:

When rotating a point \( (x, y) \) 90° clockwise, the new coordinates \( (x', y') \) can be found using the formula:
\[
(x', y') = (y, -x)
\]

Applying this to point \( H(2, -6) \):

1. Identify \( x \) and \( y \):
- \( x = 2 \)
- \( y = -6 \)

2. Apply the transformation:
- \( x' = y = -6 \)
- \( y' = -x = -2 \)

Thus, the coordinates of the image of point \( H \) after the 90° clockwise rotation about the origin are \( H'(-6, -2) \).

So the correct answer is:
\( H'(-6, -2) \).