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: $$(6,-4)$$