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 negative 4 right parenthesis

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

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

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

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 \((-4, -6)\):

- \(x = -4\)
- \(y = -6\)

Using the transformation:

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

So the new point after a 90-degree counterclockwise rotation is \((6, -4)\).

The correct response is:

\((6, -4)\) (left parenthesis 6 comma negative 4 right parenthesis)