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

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

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

(4, 6)

Answer 1

To rotate a point \((x, y)\) by 180 degrees counterclockwise around the origin, you can use the rule:

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

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

1. Change the sign of the x-coordinate: \(-(-4) = 4\)
2. Change the sign of the y-coordinate: \(-(-6) = 6\)

So, the new point after the rotation is:

\[ (4, 6) \]

Therefore, the answer is \((4, 6)\).