11 plus Coordinates & Position questions

What a Coordinates & Position question looks like

An 11 plus Coordinates & Position question names points by their coordinates and asks where something is. The answer is a position: the pair of numbers a point sits on, how many squares apart two points are, the halfway point between them, or the corner that completes a shape. The sibling topic Transformations asks what a move does to a whole shape, including turning it and counting its lines of symmetry, and neither of those appears here.

The range runs from reading one point off a numbered grid to genuinely stretching work. In between sit questions that compare two points, measure a journey in two straight legs, find a midpoint, follow a compass trail, translate a point or reflect one in a mirror line such as x = 7, and use a shape’s line of symmetry to find a missing corner. The hardest ask for the name of the quadrilateral four plotted corners make, for a fourth point on a straight line, for the pair of points that makes a parallel line, or for a shape enlarged by a scale factor. Nearly all stay in the top right quarter of the grid, with positive whole numbers.

Nearly every question is drawn on a grid with numbered axes and ruled squares, so the examples here state each point in words instead. That costs nothing: a point is (3, 4) whether or not the squares are ruled in.

Example one: naming the point a picture sits on

A small house is drawn on a grid, 2 squares along the bottom and 5 squares up the side. What are its coordinates? The options are (2, 4), (3, 5), (5, 2), (5, 3) and (2, 5).

Coordinates are read along first and then up, starting from the corner where both numbers are zero. Going along the bottom, the house is above the 2. Going up the side, it is level with the 5. Along before up, so the answer is (2, 5).

The option that catches most children is (5, 2), the same two numbers the other way round, there for anyone who reads up the side first out of habit. The other near miss is (2, 4), one square out on the count upwards, which happens when a child starts counting at the first ruled line rather than at zero.

Example two: following a trail given in compass directions

A toy robot starts at the point (8, 2). It moves 6 squares west, then 5 squares north, then 3 squares east, and finally 2 squares south. Where does it stop? The options are (5, 7), (2, 5), (5, 5), (17, 5) and (5, 9).

Take one move at a time and write the new pair down before starting the next. North and south change the second number, east and west change the first. Start at (8, 2). Six west takes the first number to 2, giving (2, 2). Five north takes the second to 7, giving (2, 7). Three east gives (5, 7). Two south takes 7 back down to 5. It stops at (5, 5).

The tempting wrong option is (5, 7), exactly where the robot is after three of the four moves. A child who does all the hard tracking and then answers a step early picks it. The other trap is (17, 5), from adding the westward moves rather than taking them away.

Example three: the corner that finishes a rectangle

A pond on a garden plan is a rectangle with sides parallel to the axes. Two opposite corners are at (3, 8) and (11, 2). Which of these is also a corner of the pond? The options are (8, 3), (3, 11), (7, 5), (11, 8) and (2, 8). This one comes as plain text with no grid, so counting squares is no help.

A rectangle like this only ever uses two different along-numbers and two different up-numbers, one of each at every corner. Here they are 3 and 11, and 8 and 2. The given corners pair 3 with 8 and 11 with 2, so the other two corners swap the partners: (3, 2) and (11, 8). Only (11, 8) is in the list.

The option that tempts is (8, 3), the first corner with its numbers the wrong way round, which happens when a child reads up before along. The option (7, 5) is the middle of the pond, the answer to a midpoint question rather than this one.

How to answer it

1. Write down every point the question names as a pair of numbers before doing anything else. Along first, then up.
2. Work out what is being asked: a position, a distance, a halfway point, or a missing corner. The options usually include a correct answer to a different one of those.
3. Do moves one at a time, writing the pair down after each. Right, east and up, north add to a number; left, west and down, south take away from it.
4. For a halfway point, add the two along-numbers and halve, then do the same with the up-numbers. An answer ending in .5 is normal.
5. Check the answer against the picture the question paints: a rectangle’s corners should line up, and a trail should end where the last direction sends it.

Common mistakes

• Swapping the two numbers. A point 2 along and 5 up is (2, 5), and (5, 2) is somewhere else entirely. The swapped pair is always one of the options, and so is the pair one square out, from counting off the first ruled line instead of from zero.
• Rounding a halfway point to a whole number. Halfway between (2, 6) and (7, 6) is (4.5, 6), and both (4, 6) and (5, 6) sit among the options for a child who thinks coordinates must be whole numbers.
• Adding when the move goes left or down. A corner at (3, 4) moved 2 squares left and 3 up lands on (1, 7). Adding both moves gives (5, 7), the classic slip on a translation.
• Handing back a number already in the question. Points at (3, 1) and (3, 6) are 5 squares apart, but 6 and 3 are both offered, and both are the answer to nothing.

How to practise 11 plus Coordinates & Position questions

The habit that pays is saying the order out loud, along and then up, until a child stops having to think about it. After that, practice should be mixed rather than repetitive: a reading question, then a midpoint, then a compass trail, so that working out what is being asked stays part of the job.

11+ Daily has a Coordinates & Position project inside its 11 plus maths practice, covering reading and plotting points, distances and midpoints, translations and compass trails, reflections, missing corners and parallel lines. Every question is original to 11+ Daily, nothing is a past paper, and nothing is licensed from another publisher. The bank is re-checked in rounds. If you are deciding how much time to give it, we have written about how much 11 plus practice a child needs each day.

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