Rotate the point (−4, −6)

Question

on a geometric figure 90 degrees counterclockwise. What is the new point?(1 point)
Responses

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

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

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

(−6, 4)

Answer 1

To rotate a point (x, y) 90 degrees counterclockwise around the origin, you can use the transformation:

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

For the point (−4, −6), we can apply this transformation:

1. Identify x and y:

   • x = -4
   • y = -6

2. Apply the transformation:

   • The new x-coordinate will be -y = -(-6) = 6
   • The new y-coordinate will be x = -4

Thus, the new point after the rotation is (6, -4).

Therefore, the correct response is:

(6, −4)