Rotate the point (−4, −6)

Question

on a geometric figure 180 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

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

(4, 6)

Answer 1

To rotate a point (x, y) 180 degrees counterclockwise around the origin, the new coordinates can be calculated using the transformation:

\[ (x', y') = (-x, -y) \]

For the point (−4, −6):

\[ x' = -(-4) = 4 \] \[ y' = -(-6) = 6 \]

Thus, the new point after rotating (−4, −6) 180 degrees counterclockwise is (4, 6).

The correct response is:

(4, 6)