Question

Rotate the point (−4, −6)
(
−
4
,

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

(−6, 4)
(
−
6
,

4
)
left parenthesis negative 6 comma 4 right parenthesis

(6, −4)
(
6
,

−
4
)
left parenthesis 6 comma negative 4 right parenthesis

(6, 4)
(
6
,

4
)
left parenthesis 6 comma 4 right parenthesis

(−6, −4)

Answer 1

To rotate the point \((-4, -6)\) 90 degrees counterclockwise, you can use the rotation rule for 90 degrees counterclockwise, which states that:

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

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

1. Identify \(x\) and \(y\):
- \(x = -4\)
- \(y = -6\)

2. Apply the rotation rule:
- New \(x\) coordinate: \(-y = -(-6) = 6\)
- New \(y\) coordinate: \(x = -4\)

So the new point after rotating 90 degrees counterclockwise is \((6, -4)\).

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