Rotate the point (−4, −6)

Question

on a geometric figure 90 degrees counterclockwise. What is the new point?

Answer 1

To rotate a point $(x,y)$ 90 degrees counterclockwise around the origin, you can use the following transformation:

$$(x,y)\to (-y,x)$$

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

1. Identify $x$ and $y$: $x=-4$ and $y=-6$.
2. Apply the transformation:
   • New $x$ coordinate: $-y=-(-6)=6$
   • New $y$ coordinate: $x=-4$

So, the new point after a 90-degree counterclockwise rotation is:

$$(6,-4)$$

Therefore, the new point is $(6,-4)$.