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A triangle has vertices W(−3,7) , Q(1,−1) , and Z(−5,−2) . Apply rotation mapping rules to find the coordinates of W′ after a 9...Question
a triangle has vertices W(-3, 7)Q(1, -1)Z(-5, -2). apply rotation mapping rules to find the coordinates of W' after a 90-degree (counterclockwise) rotation about the origin.
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GPT-4o mini
To rotate a point \( (x, y) \) 90 degrees counterclockwise about the origin, we can apply the following rotation mapping rule:
\[
(x, y) \rightarrow (-y, x)
\]
Given the coordinates of point \( W(-3, 7) \), we will apply the rotation rule:
- Here, \( x = -3 \) and \( y = 7 \).
- Applying the rule:
\[
W'(-y, x) = W'( -7, -3)
\]
So, the coordinates of \( W' \) after a 90-degree counterclockwise rotation about the origin are:
\[
W'(-7, -3)
\]
\[
(x, y) \rightarrow (-y, x)
\]
Given the coordinates of point \( W(-3, 7) \), we will apply the rotation rule:
- Here, \( x = -3 \) and \( y = 7 \).
- Applying the rule:
\[
W'(-y, x) = W'( -7, -3)
\]
So, the coordinates of \( W' \) after a 90-degree counterclockwise rotation about the origin are:
\[
W'(-7, -3)
\]
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