Rotate the point (−4, −6)

Question

on a geometric figure 180 degrees counterclockwise. What is the new point?(1 point)
Responses

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

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

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

(4, 6)

Answer 1

To rotate a point \((x, y)\) 180 degrees counterclockwise around the origin, you can use the transformation \((x, y) \rightarrow (-x, -y)\).

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

1. Negate the x-coordinate: \(-(-4) = 4\)
2. Negate the y-coordinate: \(-(-6) = 6\)

So the new point after a 180-degree rotation is \((4, 6)\).

Therefore, the answer is:

\((4, 6)\)