Determine a point image after a stated rotation about the origin.
Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere.
Practise it now
Drag the track to play the cards and watch the outline move. Then say where corner C finished.
This exercise practises rotate a coordinate alongside its own main skill, Composing Transformations.
It covers most of this skill rather than all of it.
Loading the interactive exercise. Nothing you do here is saved or scored.
A worked example
One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.
Turning a point about the origin
Point R is rotated 270 degrees clockwise about the origin. What are the coordinates of the image?
R is at (5, 1) and the centre of the turn is (0, 0).
Plotted on the grid: R at (5, 1), B at (4, 4).
(1, 5)
(-1, 5)
(-5, -1)
(1, -5)
Answer: (-1, 5)
How you get there
Turning (5, 1) three quarter turns clockwise about the origin lands on (-1, 5), which means the distance from the origin is unchanged while the direction moves round by 270 degrees.
Why the other answers tempt
A rotation keeps the point the same distance from the origin.
If they are stuck, say this
Picture the arm from (0, 0) out to R sweeping three quarter turns clockwise, and see which quarter of the grid it ends up in.
Drag the track to play the cards and watch the outline move. Then say where corner C finished.
This engine’s own main skill is Composing Transformations. It practises rotate a coordinate alongside it, and covers most of it rather than all.
The programme is “Flip in the line y = x”, then “Slide 2 right, 3 down”. Taking the cards one at a time, a flip in y = x SWAPS the two numbers: (x, y) becomes (y, x), and no sign changes at all; and then a slide adds the same pair of numbers to every corner: (x, y) becomes (x + 2, y − 3). Corner C starts at (-2, 3) and finishes at (5, -5). The order matters as much as the cards do: each card acts on wherever the shape has got to, not on where it started, so playing them the other way round can leave the shape somewhere else entirely.
Step 1. Play it. Drag the fold track all the way across to play both cards, then scrub back and forth.
Step 2. Where did it land?. Now the question: where does corner C finish?
What to say if they get stuck
Scrub the track slowly, and back again. The pale outlines show every place the shape stopped.
Follow corner C on its own rather than the whole shape - it leaves a dotted trail.
a slide adds the same pair of numbers to every corner: (x, y) becomes (x + 2, y − 3).
How rotate a coordinate differs from the skills beside it
The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: determine a point image after a stated rotation about the origin, and it stops where the centre, direction, and turn are explicit.
Apply three stated rotations or reflections in order. Exactly three transformations are composed. One-step and two-step transformations have separate skills.
Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.
Determine a point image after a stated rotation about the origin. It is one of 55 named maths skills in the 11+, in the geometry strand, and this page carries 1 interactive exercise that practises it.
A rotation keeps the point the same distance from the origin. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
Point at the next move rather than explaining the whole rule. Picture the arm from (0, 0) out to R sweeping three quarter turns clockwise, and see which quarter of the grid it ends up in.
The skill map draws the line here: The centre, direction, and turn are explicit. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
The geometry strand holds 15 skills that are tested together, and the pages next to rotate a coordinate are rotate a shape, solve an angle relation and track cube faces from a net. Each has its own exercise and its own link, and none of them needs an account.
Use The Transformation Deck, embedded on this page. It is the exercise the skill map attaches to rotate a coordinate, it runs in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. It also has its own link, so you can send it to a child without sending them anywhere else first.
Knowing which maths topic to practise is most of the work
A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.
