Question
The point Q(−5,−9) is rotated −270° about the origin. Select the location of Q′ . (1 point)
Responses
Q′(−5,9)
upper Q prime left parenthesis negative 5 comma 9 right parenthesis
Q′(9,5)
upper Q prime left parenthesis 9 comma 5 right parenthesis
Q′(5,9)
upper Q prime left parenthesis 5 comma 9 right parenthesis
Q′(9,−5)
Responses
Q′(−5,9)
upper Q prime left parenthesis negative 5 comma 9 right parenthesis
Q′(9,5)
upper Q prime left parenthesis 9 comma 5 right parenthesis
Q′(5,9)
upper Q prime left parenthesis 5 comma 9 right parenthesis
Q′(9,−5)
Answers
GPT-4o mini
To rotate the point \( Q(-5, -9) \) by \(-270^\circ\) (which is equivalent to a \(90^\circ\) positive rotation) about the origin, we can follow these steps:
1. **Understand the transformation**: When a point \((x, y)\) is rotated \(90^\circ\) counterclockwise (positive direction) about the origin, the new coordinates \((x', y')\) become:
\[
(x', y') = (-y, x)
\]
2. **Apply the transformation**: For the point \( Q(-5, -9) \):
\[
x' = -(-9) = 9
\]
\[
y' = -5
\]
Therefore, the new coordinates after the rotation is:
\[
Q'(9, -5)
\]
So the location of \( Q' \) after rotating \( Q(-5, -9) \) by \(-270^\circ\) about the origin is \(\mathbf{Q'(9, -5)}\).
1. **Understand the transformation**: When a point \((x, y)\) is rotated \(90^\circ\) counterclockwise (positive direction) about the origin, the new coordinates \((x', y')\) become:
\[
(x', y') = (-y, x)
\]
2. **Apply the transformation**: For the point \( Q(-5, -9) \):
\[
x' = -(-9) = 9
\]
\[
y' = -5
\]
Therefore, the new coordinates after the rotation is:
\[
Q'(9, -5)
\]
So the location of \( Q' \) after rotating \( Q(-5, -9) \) by \(-270^\circ\) about the origin is \(\mathbf{Q'(9, -5)}\).