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 negative 5 right parenthesis

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

(8, 5)

Answer 1

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

For a 270-degree rotation, the new coordinates \((x', y')\) are given by:
\[
(x', y') = (y, -x)
\]

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

Applying the transformation:
\[
(x', y') = (8, -5)
\]

So, the new point after rotating \((5, 8)\) by 270 degrees counterclockwise about the origin is \((8, -5)\).

The correct response is:
\((8, -5)\)