Question
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 degrees (counterclockwise) rotation about the origin.(1 point) Responses -1, 1) -1, 1) (7, 3) (7, 3) 3, -7) 3, -7) (-7, -3)
Answers
GPT-4o mini
To perform a 90 degrees counterclockwise rotation about the origin, you can use the rotation mapping rule:
\[
(x, y) \rightarrow (-y, x)
\]
For the point W(-3, 7):
1. Identify the coordinates: \(x = -3\), \(y = 7\).
2. Apply the rotation mapping:
\[
W(-3, 7) \rightarrow (-7, -3)
\]
Therefore, the coordinates of W' after a 90 degrees counterclockwise rotation about the origin are:
\[
W'(-7, -3)
\]
So, the correct response is \((-7, -3)\).
\[
(x, y) \rightarrow (-y, x)
\]
For the point W(-3, 7):
1. Identify the coordinates: \(x = -3\), \(y = 7\).
2. Apply the rotation mapping:
\[
W(-3, 7) \rightarrow (-7, -3)
\]
Therefore, the coordinates of W' after a 90 degrees counterclockwise rotation about the origin are:
\[
W'(-7, -3)
\]
So, the correct response is \((-7, -3)\).