Question

90 and 270 Degree Rotations Quick Check
2 of 52 of 5 Items
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)
Responses

(4, 6)
left parenthesis 4 comma 6 right parenthesis

(−6, 4)
left parenthesis negative 6 comma 4 right parenthesis

(−6, −4)
left parenthesis negative 6 comma negative 4 right parenthesis

(−4, 6)

Answer 1

To rotate a point \((x, y)\) 90 degrees clockwise about the origin, the new coordinates are given by the transformation:

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

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

1. Identify \(x = -4\) and \(y = -6\).
2. Apply the transformation:
- New \(x\) coordinate: \(y = -6\)
- New \(y\) coordinate: \(-x = -(-4) = 4\)

So, the new point after the rotation is \((-6, 4)\).

The correct response is \((−6, 4)\) (left parenthesis negative 6 comma 4 right parenthesis).