Question

Rotate the point (−3, −5)
on a geometric figure 270 degrees counterclockwise. What is the new point?(1 point)
Responses

( 3, 5)
left parenthesis 3 comma 5 right parenthesis

( 5, −3)
left parenthesis 5 comma negative 3 right parenthesis

(− 5, 3)
left parenthesis negative 5 comma 3 right parenthesis

( 5, 3)

Answer 1

To rotate the point \((-3, -5)\) 270 degrees counterclockwise, we can use the following rotation rules:

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

Starting with \((-3, -5)\):
1. Apply the rotation for 270 degrees counterclockwise (or 90 degrees clockwise):
\[
(y, -x) = (-5, 3)
\]

Thus, the new point after rotating \((-3, -5)\) 270 degrees counterclockwise is \((-5, 3)\).

The correct answer is:
\[
\text{(−5, 3)}
\]