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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 about the origin, you can use the following transformation:

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

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

  1. Take \(x = -7\) and \(y = 4\).
  2. Apply the transformation:
    • The new x-coordinate will be \(-y = -4\).
    • The new y-coordinate will be \(x = -7\).

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

\[ (-4, -7) \]

Thus, the answer is \((-4, -7)\).