Question

What is the new point when you rotate a geometric figure with point (5, 8)
270 degrees counterclockwise about the origin?(1 point)
Responses

(−8, −5)
left parenthesis negative 8 comma negative 5 right parenthesis

(8, 5)
left parenthesis 8 comma 5 right parenthesis

(8, −5)
left parenthesis 8 comma negative 5 right parenthesis

(−5, 8)

Answer 1

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

A 270-degree counterclockwise rotation can be understood as a 90-degree clockwise rotation. The rotation rule for a point (x, y) after a 90-degree clockwise rotation is given by the transformation:

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

So for the point (5, 8):

1. Apply the rotation:
\[
(5, 8) \rightarrow (8, -5)
\]

Therefore, the new coordinates after rotating (5, 8) by 270 degrees counterclockwise about the origin are (8, -5).

The correct response is:

\((8, -5)\)