Question

Given a point on a line segment (−4, 5) , what is the new point when the point is rotated counterclockwise about the origin 270 degrees?(1 point) ()

Answer 1

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Answer 2

To rotate a point counterclockwise about the origin, you can use the rotation transformation formulas. A rotation of \( \theta \) degrees can be done using the following formulas:

\[
x' = x \cdot \cos(\theta) - y \cdot \sin(\theta)
\]

\[
y' = x \cdot \sin(\theta) + y \cdot \cos(\theta)
\]

For a rotation of 270 degrees (which is equivalent to -90 degrees), the cosine and sine values are:

\[
\cos(270^\circ) = 0
\]
\[
\sin(270^\circ) = -1
\]

Now, applying these values to the point \((-4, 5)\):

\[
x' = -4 \cdot 0 - 5 \cdot (-1) = 0 + 5 = 5
\]
\[
y' = -4 \cdot (-1) + 5 \cdot 0 = 4 + 0 = 4
\]

Thus, the new point after rotating \((-4, 5)\) counterclockwise about the origin by 270 degrees is:

\[
(5, 4)
\]