Given a point (1, 2)

Question

on a geometric figure, what is the new point when the figure is rotated counterclockwise about the origin 90 degrees

Answer 1

To rotate a point counterclockwise about the origin by 90 degrees, you can use the following transformation formula:

If the original point is \((x, y)\), the new coordinates \((x', y')\) after a 90-degree rotation are given by:

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

For the point \((1, 2)\):

• \(x = 1\)
• \(y = 2\)

Applying the transformation:

\[ x' = -y = -2 \] \[ y' = x = 1 \]

Thus, the new point after rotating \((1, 2)\) 90 degrees counterclockwise about the origin is \((-2, 1)\).