Use rotation mapping to rotate P(4,−9)

Question

𝑃
(
4
,
−
9
)
180 degrees (counterclockwise) about the origin. What are the coordinates of P′
𝑃
′
?(1 point)
Responses

P′(−4,9)
𝑃
′
(
−
4
,
9
)
upper P prime left parenthesis negative 4 comma 9 right parenthesis

P′(4,9)
𝑃
′
(
4
,
9
)
upper P prime left parenthesis 4 comma 9 right parenthesis

P′(−9,4)
𝑃
′
(
−
9
,
4
)
upper P prime left parenthesis negative 9 comma 4 right parenthesis

P′(9,−4)

Answer 1

To rotate a point \( P(x, y) \) 180 degrees counterclockwise about the origin, you can use the following rotation rule:

\[ P'(x, y) \rightarrow P'(-x, -y) \]

For the point \( P(4, -9) \):

1. Apply the rotation rule: \[ P'(4, -9) = P'(-4, 9) \]

Thus, the coordinates of \( P' \) after a 180-degree rotation about the origin are \( P'(-4, 9) \).

The correct response is: \( P'(-4, 9) \)