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 negative 6 comma 4 right parenthesis

(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

Answer 1

To rotate a point \((x, y)\) 90 degrees counterclockwise around the origin, the new coordinates can be determined using the formula:

\[ (x', y') = (-y, x) \]

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

1. \(x' = -(-6) = 6\)
2. \(y' = -4\)

So the new coordinates after rotation are \((6, -4)\).

Thus, the answer is:

\((6, -4)\)