Apply two stated coordinate transformations in order.
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 compose coordinate transformations alongside its own main skill, Composing Transformations.
It covers most of this skill rather than all of it.
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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.
Two transformations, in order
Point A is reflected in the y-axis and then translated 1 right and 2 down. What are the coordinates of the image?
A starts at (2, 1) and the mirror line is the y-axis.
Plotted on the grid: A at (2, 1), R at (6, 2).
(-2, 1)
(3, -3)
(-1, -1)
(-3, -1)
Answer: (-1, -1)
How you get there
Reflecting (2, 1) in the y-axis gives (-2, 1), and sliding that 1 right and 2 down gives (-1, -1), which means the order matters - sliding first would land somewhere else.
Why the other answers tempt
Doing the slide before the reflection gives a different point.
If they are stuck, say this
Do the reflection first and write down where the point lands, then slide that new point 1 right and 2 down.
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 compose coordinate transformations 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 compose coordinate transformations 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: apply two stated coordinate transformations in order, and it stops where exactly two transformations are composed. Single transformations have separate skills.
Apply three stated rotations or reflections in order. Exactly three transformations are composed. One-step and two-step transformations have separate skills.
Questions parents ask about compose coordinate transformations
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.
Apply two stated coordinate transformations in order. 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.
Doing the slide before the reflection gives a different point. 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. Do the reflection first and write down where the point lands, then slide that new point 1 right and 2 down.
The skill map draws the line here: Exactly two transformations are composed. Single transformations have separate skills. 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 compose coordinate transformations are identify a cube net, identify a shape property and identify line symmetry. 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 compose coordinate transformations, 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.
