Question
Given a point (1, 2)
on a geometric figure, what is the new point when the figure is rotated counterclockwise about the origin 90 degrees?(1 point)
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)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To rotate a point (x, y) counterclockwise about the origin by 90 degrees, the new coordinates (x', y') can be found using the following transformation:
\[
x' = -y
\]
\[
y' = x
\]
So, if we apply this transformation to the point (1, 2):
- \( x' = -y = -2 \)
- \( y' = x = 1 \)
Thus, the new point after rotating (1, 2) counterclockwise about the origin by 90 degrees is (-2, 1).
So the answer is:
\[
(-2, 1)
\]
\[
x' = -y
\]
\[
y' = x
\]
So, if we apply this transformation to the point (1, 2):
- \( x' = -y = -2 \)
- \( y' = x = 1 \)
Thus, the new point after rotating (1, 2) counterclockwise about the origin by 90 degrees is (-2, 1).
So the answer is:
\[
(-2, 1)
\]
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