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 \((x, y)\) counterclockwise about the origin by 90 degrees, you can use the following transformation of the coordinates:

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

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

1. Substitute \(x = 1\) and \(y = 2\) into the transformation: \[ (-y, x) = (-2, 1) \]

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