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

Answer 1

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

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

Starting with the point \( (-4, -6) \):

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

So, the new coordinates after the rotation will be:

\[
(6, -4)
\]

Thus, the answer is \( (6, -4) \).