Question

Rotate the point (−4, −6)
on a geometric figure 90 degrees counterclockwise. What is the new point?(1 point)
Responses

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

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

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

(−6, 4)

Answer 1

To rotate the point \( (-4, -6) \) 90 degrees counterclockwise, you can use the rotation formula for a point \((x, y)\):

- The new coordinates after a 90-degree counterclockwise rotation will be \((-y, x)\).

Applying this to the point \( (-4, -6) \):

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

So, the new point will be:
\[
(-(-6), -4) = (6, -4)
\]

Therefore, the new point after a 90-degree counterclockwise rotation is:

\((6, -4)\).

So the correct response is:
\((6, -4)\).