Question

(-4,5) rotate counterclockwise 270 degrees

Answer 1

To rotate the point \((-4, 5)\) counterclockwise by 270 degrees, you can first recognize that a 270-degree rotation counterclockwise is equivalent to a 90-degree rotation clockwise.

To rotate a point \((x, y)\) 90 degrees clockwise, the new coordinates \((x', y')\) can be found using the following transformation:

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

Now, let's apply this transformation to the point \((-4, 5)\):

1. Take the original coordinates:
\[
x = -4, \quad y = 5
\]

2. Apply the transformation:
\[
x' = y = 5
\]
\[
y' = -x = -(-4) = 4
\]

So, after a 90-degree clockwise rotation, the new coordinates are \((5, 4)\).

Thus, the point \((-4, 5)\) rotated counterclockwise by 270 degrees is \(\boxed{(5, 4)}\).