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Given a point (−7, 4)

on a geometric figure, what is the new point after rotating the figure 90 degrees counterclockwise?

1 answer

To rotate a point \((x, y)\) 90 degrees counterclockwise around the origin, we can use the rotation transformation formula. The new coordinates \((x', y')\) after rotation are given by:

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

For the point \((-7, 4)\):

  1. \(x = -7\)
  2. \(y = 4\)

Applying the formula:

\[ x' = -y = -4 \] \[ y' = x = -7 \]

Therefore, the new point after rotating \((-7, 4)\) 90 degrees counterclockwise is:

\[ \boxed{(-4, -7)} \]