"I added 3 to the x and 3 to the y, so (2, 4) becomes (5, 7)."
For a dilation about the origin, the child adds the scale factor k to each coordinate instead of multiplying. With k = 3 and point (2, 4), they write (2 + 3, 4 + 3) = (5, 7) instead of (3 × 2, 3 × 4) = (6, 12).
They just learned translation rules, where you add the same amount to each coordinate. They carry that adding habit over to dilations without noticing that dilation stretches by multiplying.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
Scales only one coordinate
What you might hear
"I doubled the x to get 6, so (3, 5) becomes (6, 5)."
The child multiplies only the x-coordinate (or only the y) by the scale factor and leaves the other one alone. With k = 2 and point (3, 5), they write (6, 5) instead of (6, 10).
They stop after the first multiplication, or they treat the rule like a one-axis stretch. They forget that a dilation grows the figure in both directions at once.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
Thinks a scale factor less than 1 enlarges
What you might hear
"A dilation makes it bigger, so (8, 6) can't shrink to (4, 3)."
The child believes any dilation makes the figure bigger, so with k = 1/2 they expect point (8, 6) to move farther out. The correct image (4, 3) is closer to the origin, but they reject it as too small.
They link the word 'dilation' only with growing, the way pupils dilate to get larger. They never connected that k between 0 and 1 shrinks the figure.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
What to say when you see it
For each mistake above, Algo School gives you the words to say next — the specific response that corrects the thinking instead of just marking the answer wrong, plus practice aimed at that exact error.
Reason about the image of (6, 4) after a dilation centered at the origin with scale factor of 2, for Noah.
A(6, 8)
B(12, 4)
C(12, 8)
D(8, 6)
AnswerC — (12, 8)
Generated by coordinate-plane-8, a deterministic question engine — not written by an AI, and verified before any child sees it.
FAQ
Questions parents ask about this
How do I know which of these mistakes my child is making?
Look at what they SAY, not just what they wrote. Each mistake above includes the phrasing a parent typically hears — that sentence is usually the giveaway. In Algo School, the tutor recognises these patterns while your child is working and adapts the session around the one it sees.
Is "Apply coordinate rules for dilations" something children normally struggle with?
Yes. We track 3 distinct approved mistake patterns for this concept, each one written up because it recurs — not because it is unusual. A child making one of them is doing something systematic, which is far easier to fix than random errors.
What should I do once I know which mistake it is?
Respond to the thinking, not the answer. Algo School gives parents the specific wording for each mistake, then generates practice targeted at that error and shows you whether it actually cleared.
Where do these mistakes come from?
They are part of the same content library that drives practice: each one is reviewed and approved before it is used, and the Geometry questions on this site are checked by an automated verification pass before a child is ever served them.
Related
Other places children go wrong
Where this sits
The year this concept belongs to
See the full curriculum map — every Common Core concept we cover, the
verified question count, and what a child at this level should know.
Find out which one it actually is
Free for 15 days — a card is kept on file, but $0 is charged until
the trial ends. Cancel in one click before then and pay nothing.