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)

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 \( (-4, -6) \):

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

Now apply the transformation:

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

So, the new point after the 90 degrees counterclockwise rotation is:

\[ (6, -4) \]

The correct response is:

(6, −4).