Rotate the point (−4, −6)

Question

(
−
4
,

−
6
)
on a geometric figure 90 degrees counterclockwise. What is the new point?(1 point)
Responses

(6, −4)
(
6
,

−
4
)
left parenthesis 6 comma negative 4 right parenthesis

(−6, 4)
(
−
6
,

4
)
left parenthesis negative 6 comma 4 right parenthesis

(6, 4)
(
6
,

4
)
left parenthesis 6 comma 4 right parenthesis

(−6, −4)

Answer 1

To rotate the point \((-4, -6)\) 90 degrees counterclockwise, we can use the rotation transformation for points in the Cartesian plane. The transformation for a point \((x, y)\) rotated 90 degrees counterclockwise around the origin is \((-y, x)\).

Applying this to the point \((-4, -6)\):

1. Identify \(x\) and \(y\):

   • \(x = -4\)
   • \(y = -6\)

2. Apply the transformation: \[ \text{New } x = -y = -(-6) = 6 \] \[ \text{New } y = x = -4 \]

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

Thus, the correct response is: \[ (6, -4) \]