Brainblox brainblox Play Brainblox →
11+ question-type guides ›

Maths: Coordinates and Transformations

▶  Watch: how to read and move coordinates6 min

Four steps in about six minutes — one real question, worked step by step, then the traps to watch out for.

In these questions, you're given a grid with numbers along its edges, and some points marked with letters.

Your job is to find a point's coordinates: the pair of numbers that says where it is. Sometimes the point moves first, by a translation or a reflection. There are five answers to choose from.

In GL's papers the points always sit where grid lines cross, and the numbers label the lines, not the squares. But GL draws its grids in different ways on purpose, so read each one. The video above and the worked example below work through the same question, with the options in the same order. Then both work a second, short question: a reflection, on the same four steps.

The method

Four steps: read the axes, across first, then up, check the point.

  1. Step 1 of 4

    Read the axes

    Before you count, find zero, and see how the numbers go up. Do they go up in ones or twos?
  2. Step 2 of 4

    Across first

    The first number says how far across. Start at zero, and count the lines along the bottom until you're right below the point.
  3. Step 3 of 4

    Then up

    The second number says how far up. From there, count up the side to the point, line by line.
  4. Step 4 of 4

    Check the point

    It should sit right where two lines cross. Swapped, would the pair land somewhere else?

Worked example

Point Q is marked on the grid. What are its coordinates?

The grid: numbered 0 to 8 along the bottom and 0 to 8 up the side, with 0 in the corner where the axes meet. Five lettered points sit where lines cross: K at (6, 6), P at (5, 3), M at (3, 6), G at (3, 1), and Q on the same up-and-down line as M and G, 2 lines below M.

A. (4, 4) B. (3, 6) C. (3, 5) D. (3, 4) E. (4, 3)

  1. Read the axes. Here, zero is in the corner, where the two axes meet. The numbers go up in ones, along the bottom and up the side. Each number sits on a line, not in a square, and every point sits where two lines cross.
  2. Across first. Start at zero, and count the lines along the bottom until you're right below Q: 1, 2, 3. So the first number is 3.
  3. Then up. From there, count up to Q, line by line: 1, 2, 3, 4. The side says 4 as well, so Q is at (3, 4).
  4. Check the point. It should sit right where two lines cross, and (3, 4) does: it's Q. Now swap the numbers. (4, 3) would be 4 across, then 3 up, and that lands on an empty crossing, not on Q. That's E, the pair swapped, so E is out. A and C each land one line away from Q, so cross them off. And B is (3, 6), which is point M, two lines further up. So B is out too. So the answer is D.

Answer: D — (3, 4) (3 across, then 4 up: point Q)

A second worked example

The same four steps work when a point moves.

Point Q is the reflection of point P in a mirror line. Which line is the mirror line?

The grid: numbered 0 to 12 along the bottom and 0 to 10 up the side, with 0 in the corner. P is at (8, 1) and Q is at (8, 9). Five lines are drawn. N, L, K and M run straight across, at 1 up (through P), 4 up, 5 up and 6 up. J runs straight up and down, at 10 across.

A. line J B. line M C. line L D. line K E. line N

  1. Read the axes. Zero's in the corner, and the numbers go up in ones.
  2. Across first. P and Q are both 8 across, so the path between them runs straight up, and the mirror line must cut straight across it. Line J runs up and down, like the path, so J is out.
  3. Then up. P is 1 up, and Q is 9 up. That's 8 lines apart, so halfway is 4 lines from each, at 5 up. That's line K.
  4. Check the point. P is 4 lines below K, so its reflection is 4 lines above K, at 9 up, right on Q. M and L are each one line off halfway, so cross them off. And N goes through P itself, so N is out. So the answer is D.

Answer: D — line K (halfway between P (8, 1) and Q (8, 9))

Things to watch out for

  1. Across first, then up. The swapped pair can land on a real point. Which point is at (4, 2)? 4 across, then 2 up, lands on P. Go up first by mistake, and you land on T instead: a real point, and one of the answers. Swapped pairs like this come up again and again.
  2. Count the lines, not the squares. Points sit where lines cross, and the numbers label the lines. Lose count by one, and you land one line out, like A and C in the worked example. Some grids go up in twos, so check before you count. If the numbers along the bottom of that grid went up in twos, Q's line would read 6, even though it's still 3 squares along.
  3. The mirror is halfway. Halfway between a point and its reflection. Point A is reflected in an up-and-down mirror line. A is 2 squares from the mirror line, so its reflection is 2 squares past it, on the other side: point S. Q stops just 1 square past the mirror, and P goes twice as far.
  4. Double the sides, not the coordinates. The shape grows from the corner that stays still. Rectangle ABCD has corner A at (1, 2) and corner C at (5, 5). It is 4 squares across and 3 up. With every side twice as long, it's 8 across and 6 up, growing from corner A, which stays where it is. So C ends up at (9, 8). Doubling C's own numbers gives (10, 10). That grows the shape from zero, not from A.

Related

All example questions come from the Brainblox question bank — practise this question type inside 25+ learning games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.