Question

tate the point (−4, −6)
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 the point \((-4, -6)\) 90 degrees counterclockwise around the origin, you can use the following transformation:

If you have a point \((x, y)\), after a 90-degree counterclockwise rotation, the new coordinates \((x', y')\) will be:
\[
(x', y') = (-y, x)
\]

For the point \((-4, -6)\):
- \(x = -4\)
- \(y = -6\)

Using the transformation:
\[
x' = -(-6) = 6
\]
\[
y' = -4
\]
Thus, the new coordinates are \((6, -4)\).

The correct response is:
\((6, -4)\)