Question

Rotate the point (5, 8) on a geometric figure 270 degrees clockwise. What is the new point? (1 point)

(8,-5)

(-8,5)

(-8,-5)

(8, 5)

Answer 1

To rotate the point (5, 8) by 270 degrees clockwise, we can use the rules for rotation in the Cartesian coordinate system.

270 degrees clockwise is equivalent to a 90 degrees counterclockwise rotation. The rule for a 90-degree counterclockwise rotation is:

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

Applying this to the point (5, 8):

1. Take the y-coordinate (8) and make it negative: \(-8\)
2. Take the x-coordinate (5) and move it to the y-position: \(5\)

Thus, the new coordinates after the rotation will be:

\[
(5, 8) \rightarrow (-8, 5)
\]

Therefore, the new point after rotating (5, 8) by 270 degrees clockwise is \((-8, 5)\).

The answer is \((-8, 5)\).