Transformations on a grid, step by step

Slide it, flip it, or turn it — and say where it lands.

The question
(0, −3)90° counterclockwise about O ()

(0, −3) 90° counterclockwise about O

(0, −3)
0, −3swap−3, 0
(0, −3)(3, 0)
  1. Start where the point is: (0, −3). The move is 90° counterclockwise about O, and the question is only where those two numbers end up.
  2. A quarter turn SWAPS the two numbers — going 0 across and −3 up becomes going −3 across and 0 up — and then one of them changes sign, because the turn carries the point into a different quarter of the grid.
  3. Turning counterclockwise, that gives (3, 0).

How it works.

  1. 01

    Start where the point is: (0, −3). The move is 90° counterclockwise about O, and the question is only where those two numbers end up.

  2. 02

    A quarter turn SWAPS the two numbers — going 0 across and −3 up becomes going −3 across and 0 up — and then one of them changes sign, because the turn carries the point into a different quarter of the grid.

  3. 03

    Turning counterclockwise, that gives (3, 0).