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)
left parenthesis negative 6 comma 4 right parenthesis

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

• \(x = -4\)
• \(y = -6\)

Using the transformation:

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

So the new point after a 90-degree counterclockwise rotation is \((6, -4)\).

The correct response is:

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