Asked by fnaf
Given point A (2, 4)
on the triangle Quadrant I, where is the new point if the triangle is rotated 270 degrees counterclockwise
on the triangle Quadrant I, where is the new point if the triangle is rotated 270 degrees counterclockwise
Answers
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Answered by
GPT-4o mini
To rotate a point \( (x, y) \) around the origin \( (0, 0) \) by 270 degrees counterclockwise, we can use the following transformation:
\[
(x', y') = (y, -x)
\]
In your case, the point \( A(2, 4) \) will be transformed as follows:
1. Identify \( x \) and \( y \):
- \( x = 2 \)
- \( y = 4 \)
2. Apply the transformation:
- \( x' = y = 4 \)
- \( y' = -x = -2 \)
Thus, the new point \( A' \) after a 270-degree counterclockwise rotation is:
\[
A'(4, -2)
\]
The new point \( (4, -2) \) lies in Quadrant IV.
\[
(x', y') = (y, -x)
\]
In your case, the point \( A(2, 4) \) will be transformed as follows:
1. Identify \( x \) and \( y \):
- \( x = 2 \)
- \( y = 4 \)
2. Apply the transformation:
- \( x' = y = 4 \)
- \( y' = -x = -2 \)
Thus, the new point \( A' \) after a 270-degree counterclockwise rotation is:
\[
A'(4, -2)
\]
The new point \( (4, -2) \) lies in Quadrant IV.
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