TransformationsRotating about the origin
Name: Date:
Rotate each point about the origin. Write where it lands.
1180° about O ()
290° clockwise about O ()
390° clockwise about O ()
4180° about O ()
590° counterclockwise about O ()
6180° about O ()
Rotations worksheets
A rotation turns a point about the origin, and the quarter turns are the ones with clean coordinate rules. These free printable worksheets ask where a point lands after a turn, with the starting point drawn on the grid.
Kid stuck on one? You don’t just get the sheet.
Rotations
The answer key prints on a separate page.
What's on this sheet
A quarter turn swaps the two numbers before either changes sign, and that swap is the part the usual notation hides. (2, 5) turned a quarter counterclockwise becomes (−5, 2): the 2 and the 5 have traded places and one has picked up a minus. A child who has seen the swap can rebuild the rule; one who has memorized four cases cannot.
Why this sheet works
A half turn is the easy one and worth doing first — both signs flip and nothing swaps, because turning 180° sends every point straight through the origin to the opposite side. Starting there gives a child one case they are sure of to check the harder ones against.
How this one works
One question from this sheet, worked through a step at a time.
(0, −2) 180° about O
(0, −2)
(0, −2)→(0, 2)
(0, −2)→(0, 2)
- Start where the point is: (0, −2). The move is 180° about O, and the question is only where those two numbers end up.
- Half a turn sends every point straight through the origin and out the other side, the same distance away. Both coordinates keep their size and swap sign.
- So (0, −2) lands on (0, 2).