Coordinates, translation and reflection
Maths · Key Stage 2 · The School
Along the corridor, up the stairs
A coordinate pair gives a position on a grid: (3, 5) means 3 across and 5 up, from the ORIGIN at (0, 0). The x-coordinate always comes first. Reversing them gives a real point, just the wrong one, which is why the order is a convention everybody keeps to — the same rule as a map grid reference.
Translation slides it
A TRANSLATION moves every point of a shape the same distance in the same direction. Nothing rotates, nothing flips, nothing changes size — the shape is identical, just elsewhere. Describe it by how far right or left and how far up or down: "translate 4 right and 2 down". Add those numbers to every vertex's coordinates and you have the new shape.
Reflection flips it
A REFLECTION produces a mirror image across a MIRROR LINE. Every point ends up the same distance from the line as it started, on the other side, measured at right angles to the line. A point sitting on the mirror line does not move. Unlike a translation, a reflection swaps left and right — so a shape and its reflection cannot usually be slid onto each other.
A triangle has vertices at (1, 1), (3, 1) and (1, 4). Translate it 4 right and 2 up: add 4 to every x and 2 to every y, giving (5, 3), (7, 3), (5, 6). The shape is identical, just moved. Now reflect the ORIGINAL in the line x = 5: the point (1, 1) is 4 to the left of the line, so its image is 4 to the right, at (9, 1). Likewise (3, 1) → (7, 1) and (1, 4) → (9, 4). Measure each distance from the mirror line, every time.