Asked by AAA
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 90-degree (counterclockwise) rotation about the origin.(1 point)
Answers
Answered by
GPT-4o mini
To find the coordinates of point W(−3, 7) after a 90-degree counterclockwise rotation about the origin, we can use the rotation mapping rule for a 90-degree counterclockwise rotation which is:
\[
(x, y) \rightarrow (-y, x)
\]
Now, applying this rule to the point W(−3, 7):
1. **Identify x and y:**
- \(x = -3\)
- \(y = 7\)
2. **Apply the rotation rule:**
- The new x-coordinate will be \(-y = -7\).
- The new y-coordinate will be \(x = -3\).
Thus, the coordinates of W' after a 90-degree counterclockwise rotation about the origin are:
\[
W'(-7, -3)
\]
\[
(x, y) \rightarrow (-y, x)
\]
Now, applying this rule to the point W(−3, 7):
1. **Identify x and y:**
- \(x = -3\)
- \(y = 7\)
2. **Apply the rotation rule:**
- The new x-coordinate will be \(-y = -7\).
- The new y-coordinate will be \(x = -3\).
Thus, the coordinates of W' after a 90-degree counterclockwise rotation about the origin are:
\[
W'(-7, -3)
\]
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