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 negative 6 comma 4 right parenthesis

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

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

(−6, −4)

Answer 1

To rotate a point \( (x, y) \) 90 degrees counterclockwise around the origin, you can use the transformation:

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

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

1. \( x = -4 \)
2. \( y = -6 \)

Now apply the transformation:

\[
(-4, -6) \rightarrow (6, -4)
\]

So, the new point after the 90 degrees counterclockwise rotation is:

\[
(6, -4)
\]

The correct response is:

**(6, −4)**.