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Rotate the point (-4,6) on a geometric figure 90 degrees counterclockwise. What is the new point? (

(-6, 4)

(6, 4)

(6,-4)

(-6,-4)

1 answer

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

\[ (x, y) \rightarrow (-y, x) \]

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

  1. Take the \(y\) coordinate (6), multiply by -1: \(-6\)
  2. Take the \(x\) coordinate (-4): stays the same in the new y position.

Thus, the new coordinates after the rotation are:

\[ (-6, -4) \]

So, the new point after rotating \((-4, 6)\) 90 degrees counterclockwise is:

\[ \boxed{(-6, -4)} \]