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

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

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

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

(−8, −5)

Answer 1

To rotate a point \((x, y)\) counterclockwise by \(270\) degrees about the origin, we can follow the rule for rotation:

- A \(90\) degrees counterclockwise rotation transforms the point \((x, y)\) to \((-y, x)\).
- A \(180\) degrees counterclockwise rotation transforms the point \((x, y)\) to \((-x, -y)\).
- A \(270\) degrees counterclockwise rotation is equivalent to a \(90\) degrees clockwise rotation, which transforms the point \((x, y)\) to \((y, -x)\).

Using the point \((5, 8)\):

1. For \(270\) degrees counterclockwise rotation (or \(90\) degrees clockwise):
\[
(5, 8) \rightarrow (8, -5)
\]

Thus, the new point after a \(270\) degrees rotation counterclockwise about the origin is \((8, -5)\).

The correct response is:

\((8, -5)\)