Rotate a point on a line at (−4, 6)

Question

180°
counterclockwise. What is the resulting point?(1 point)
Responses

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

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

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

(6, −4)

Answer 1

To rotate a point \(180^\circ\) counterclockwise around another point, you can use the following method:

1. Identify the point to rotate (in this case, \((−4, 6)\)).
2. Since you're rotating \(180^\circ\) relative to the point itself, the resulting point will have the same coordinates but their signs flipped.

So for the point \((−4, 6)\):

• The x-coordinate will change from \(-4\) to \(+4\).
• The y-coordinate will change from \(6\) to \(-6\).

Thus, the resulting point after a \(180^\circ\) rotation of the point \((−4, 6)\) is:

\((4, -6)\).

Therefore, the correct response is:

\((4, -6)\) (left parenthesis 4 comma negative 6 right parenthesis).