What is the new point when you rotate a geometric figure with point (5, 8)

Question

270 degrees counterclockwise about the origin?(1 point)
Responses

(−8, −5)

(−5, 8)

(8, −5)

(8, 5)

Answer 1

To find the coordinates of the point (5, 8) after a 270-degree counterclockwise rotation about the origin, we can use the rotation rules for the Cartesian plane.

A 270-degree counterclockwise rotation corresponds to a 90-degree clockwise rotation. The transformation for a 90-degree clockwise rotation of the point (x, y) is given by:

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

Applying this to the point (5, 8):

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

Therefore, the new coordinates after the rotation are (8, -5).

So the correct response is:

(8, -5)