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

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

(8, −5)

Answer 1

To rotate a point \((x, y)\) counterclockwise by \(270\) degrees around the origin, you can use the following formula:

\[
(x', y') = (y, -x)
\]

where \((x', y')\) are the coordinates of the new point after the rotation.

Given the point \((5, 8)\):
- \(x = 5\)
- \(y = 8\)

Applying the formula:

\[
(x', y') = (8, -5)
\]

So, the new coordinates after a \(270\)-degree counterclockwise rotation about the origin are:

\((8, -5)\)

Therefore, the correct response is:

\((8, -5)\)