Question
A traingle has vertices W (-4,7), Q (-1,-1) and Z (-7,2). Apply rotation mapping Rules to find the coordinates of W' after a 90- degree rotation about the orgin.
Answers
GPT-4o mini
To find the coordinates of point \( W' \) after a 90-degree rotation around the origin, we can use the rotation mapping rules. For a 90-degree counterclockwise rotation about the origin, the transformation rule for a point \( (x, y) \) is given by:
\[
(x, y) \rightarrow (-y, x)
\]
Given the coordinates of point \( W(-4, 7) \):
1. Identify \( x \) and \( y \):
- \( x = -4 \)
- \( y = 7 \)
2. Apply the rotation rule:
- \( W' = (-y, x) \)
- This gives us \( W' = (-7, -4) \)
Thus, after a 90-degree counterclockwise rotation about the origin, the coordinates of \( W' \) are \( \boxed{(-7, -4)} \).
\[
(x, y) \rightarrow (-y, x)
\]
Given the coordinates of point \( W(-4, 7) \):
1. Identify \( x \) and \( y \):
- \( x = -4 \)
- \( y = 7 \)
2. Apply the rotation rule:
- \( W' = (-y, x) \)
- This gives us \( W' = (-7, -4) \)
Thus, after a 90-degree counterclockwise rotation about the origin, the coordinates of \( W' \) are \( \boxed{(-7, -4)} \).