Question
Question
A segment has endpoints X(−10,0) and Y(−2,6) . Consider its image after a 180° (counterclockwise) rotation about the origin. Select the coordinates of Y′ .(1 point)
Responses
Y′(2,−6)
upper Y prime left parenthesis 2 comma negative 6 right parenthesis
Y′(6,−2)
upper Y prime left parenthesis 6 comma negative 2 right parenthesis
Y′(−6,2)
upper Y prime left parenthesis negative 6 comma 2 right parenthesis
Y′(−2,−6)
upper Y prime left parenthesis negative 2 comma negative 6 right parenthesis
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A segment has endpoints X(−10,0) and Y(−2,6) . Consider its image after a 180° (counterclockwise) rotation about the origin. Select the coordinates of Y′ .(1 point)
Responses
Y′(2,−6)
upper Y prime left parenthesis 2 comma negative 6 right parenthesis
Y′(6,−2)
upper Y prime left parenthesis 6 comma negative 2 right parenthesis
Y′(−6,2)
upper Y prime left parenthesis negative 6 comma 2 right parenthesis
Y′(−2,−6)
upper Y prime left parenthesis negative 2 comma negative 6 right parenthesis
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Answers
GPT-4o mini
To find the coordinates of point \(Y\) after a 180° counterclockwise rotation about the origin, you can use the formula for rotation. A point \((x, y)\) rotated 180° around the origin transforms to \((-x, -y)\).
The coordinates of point \(Y\) are \((-2, 6)\). Applying the rotation:
\[
Y' = (-(-2), -6) = (2, -6)
\]
Thus, the coordinates of \(Y'\) after the rotation are \(Y'(2, -6)\).
The correct response is:
**Y′(2,−6)**
The coordinates of point \(Y\) are \((-2, 6)\). Applying the rotation:
\[
Y' = (-(-2), -6) = (2, -6)
\]
Thus, the coordinates of \(Y'\) after the rotation are \(Y'(2, -6)\).
The correct response is:
**Y′(2,−6)**