Question

The point Q(−5,−9)
is rotated −270°
about the origin. Select the location of Q′
. (1 point)
Responses

Q′(9,−5)
upper Q prime left parenthesis 9 comma negative 5 right parenthesis

Q′(5,9)
upper Q prime left parenthesis 5 comma 9 right parenthesis

Q′(9,5)
upper Q prime left parenthesis 9 comma 5 right parenthesis

Q′(−5,9)

Answer 1

To rotate the point \( Q(-5, -9) \) by \( -270^\circ \) about the origin, we can convert the angle to a standard positive angle for easier calculations.

A rotation of \( -270^\circ \) is equivalent to a rotation of \( 90^\circ \) in the positive direction (since \( -270 + 360 = 90 \)).

When rotating a point \( (x, y) \) by \( 90^\circ \) counterclockwise about the origin, the new coordinates can be found using the transformation:
\[
(x', y') = (-y, x)
\]

Applying this transformation:

1. Start with \( Q(-5, -9) \):
- \( x = -5 \)
- \( y = -9 \)

2. Use the rotation formula:
- \( x' = -y = -(-9) = 9 \)
- \( y' = x = -5 \)

Thus, the new coordinates after the rotation are \( Q'(9, -5) \).

The location of \( Q' \) is \( \mathbf{Q'(9, -5)} \).