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 negative 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 the point \((-4, -6)\) 90 degrees counterclockwise, you can use the following formula for rotation:

If a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, the new coordinates \((x', y')\) will be:

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

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

1. Identify \(x\) and \(y\): \(x = -4\), \(y = -6\)
2. Apply the rotation formula:

\[ x' = -y = -(-6) = 6 \] \[ y' = x = -4 \]

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

The correct answer is \((6, -4)\).