11+ Coordinates: Ordered Pairs, Moves and Missing Vertices

The points (2, 5) and (5, 2) use the same numbers but describe different positions. An ordered pair is an instruction with a fixed order. Learning to keep the two coordinates separate makes grid questions much easier to check.

These original explanations and questions support preparation for 11-plus exams taken in 2027. They are not official papers or a complete school syllabus. Check your target school’s guidance and try each question before opening the explanation. Written English models show a supported response, not the only acceptable wording.

Agree the grid conventions

Throughout this guide the axes meet at the origin (0, 0). Positive x runs right and positive y runs up. One unit has the same scale in both directions. The first coordinate measures horizontal position; the second measures vertical position. Negative x is left of the origin and negative y is below it. Sketch a small labelled grid when it helps.

Worked example: translate one coordinate at a time

Translate (−2, 5) four units right and seven units down. The horizontal instruction gives x = −2 + 4 = 2. The vertical instruction gives y = 5 − 7 = −2. The new point is (2, −2). A translation can cross an axis and change a coordinate’s sign; it simply moves every point by the same displacement without turning the shape.

Worked example: axis reflections

Reflect (3, −4) in the y-axis. The point keeps its vertical position but moves to the opposite horizontal side, giving (−3, −4). Reflect the original point in the x-axis instead and it becomes (3, 4). These rules concern the named coordinate axes; a different mirror line requires a different check.

Use the stated shape properties

A rectangle has consecutive vertices (1, 2), (6, 2) and (6, 5), with sides parallel to the axes. The missing vertex is (1, 5): it lines up vertically with the first point and horizontally with the third. Without the axis-parallel condition, do not blindly combine coordinates from arbitrary corners.

Eight original coordinate questions

Check a result geometrically

A reflection in the y-axis should leave equal distances on opposite sides of that axis. A purely horizontal move should leave y unchanged. A midpoint should sit halfway between both corresponding coordinates. These relationships give an independent check beyond repeating the same arithmetic. They also help explain why a tempting swapped answer is wrong.

Choose a useful next step

Review negative numbers for moving through zero and missing angles for reasoning from geometric properties. Return to the maths learning hub or explore original practice and worked answers.

Sources and scope

The DfE programme of study provides a curriculum reference, not a promise about every school’s test. Examples and questions on this page are original; no school affiliation or educator endorsement is implied.