Question

Triangle JMH is rotated -270 degrees clockwise about the origin. Apply rotation mapping rules to find the image of H.
Point J: (-3, 2)
Point M: (3, 0)
Point H: (-1, -8)

Answer 1

To find the image of point H after a -270 degrees clockwise rotation about the origin, we can apply the standard rotation rule for a point (x, y).

The rule for rotating a point (x, y) counterclockwise by an angle θ is given by:

\[
(x', y') = (x \cos \theta - y \sin \theta, x \sin \theta + y \cos \theta)
\]

For a clockwise rotation, we can use the equivalent negative angle (i.e., -270 degrees is the same as +90 degrees). Therefore, we will apply the rotation for +90 degrees.

In degrees, the rotation angles work out as follows:

- \(\cos(90^\circ) = 0\)
- \(\sin(90^\circ) = 1\)

Applying the rotation transformation to the point H (-1, -8):

1. Substitute \(x = -1\) and \(y = -8\):
\[
x' = -1 \cdot 0 - (-8) \cdot 1 = 0 + 8 = 8
\]
\[
y' = -1 \cdot 1 + (-8) \cdot 0 = -1 + 0 = -1
\]

Thus, after the -270 degrees clockwise rotation, the image of point H is:

\[
H' = (8, -1)
\]

So, the final result is:

**H' = (8, -1)**.