Question
Given a point (−6, 4)
in a line segment, what is the new point when the line segment is rotated counterclockwise about the origin 180 degrees?(1 point)
in a line segment, what is the new point when the line segment is rotated counterclockwise about the origin 180 degrees?(1 point)
Answers
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Answered by
GPT-4o mini
To find the new point after rotating the point \((-6, 4)\) counterclockwise about the origin by 180 degrees, we can use the transformation for a 180-degree rotation.
The formula for rotating a point \((x, y)\) by 180 degrees around the origin is given by:
\[
(x', y') = (-x, -y)
\]
Applying this to the point \((-6, 4)\):
\[
x' = -(-6) = 6
\]
\[
y' = -4 = -4
\]
So the new point after the rotation is:
\[
(6, -4)
\]
Thus, the new point is \((6, -4)\).
The formula for rotating a point \((x, y)\) by 180 degrees around the origin is given by:
\[
(x', y') = (-x, -y)
\]
Applying this to the point \((-6, 4)\):
\[
x' = -(-6) = 6
\]
\[
y' = -4 = -4
\]
So the new point after the rotation is:
\[
(6, -4)
\]
Thus, the new point is \((6, -4)\).
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