Question

Given a point on a line segment (−4, −6) , what is the new point when the point is rotated clockwise about the origin 90 degrees?(1 point)

(−4, 6)
(−6, −4)
(4, 6)
(−6, 4)

Answer 1

To rotate a point \((x, y)\) by 90 degrees clockwise about the origin, you can use the transformation:

\[
(x, y) \rightarrow (y, -x)
\]

For the point \((-4, -6)\):

1. Replace \(x\) with \(-6\) (the original \(y\)).
2. Replace \(y\) with \(-(-4)\) (the negative of the original \(x\)).

So, the new coordinates after rotation will be:

\[
(-6, 4)
\]

Thus, the new point when \((-4, -6)\) is rotated 90 degrees clockwise about the origin is \((-6, 4)\).

The correct answer is \((-6, 4)\).