Question

Rotate a point on a line at (−4, 6)
180°
counterclockwise. What is the resulting point?(1 point)
Responses

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

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

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

(6, −4)

Answer 1

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

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

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

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

Applying the rotation:

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

Therefore, the resulting point after a \( 180^\circ \) counterclockwise rotation is \( (4, -6) \).

So, the correct response is:

(4, −6)