Coordinates, Translation & Reflection for KS2

Position and movement questions come up every year on the reasoning papers. Your child needs to read and plot coordinates confidently, translate shapes on a grid, and reflect them across a mirror line. The good news is that once the basics click, these questions are some of the most satisfying marks to pick up.

Reading and Plotting Coordinates

A coordinate is written as (x, y). The x value tells you how far across to go; the y value tells you how far up. “Along the corridor and up the stairs” is the classic way to remember it.

(3, 5) means: 3 along, 5 up

(-2, 4) means: 2 to the left, 4 up

In Year 6, children need to work with all four quadrants — that means negative coordinates too. The x-axis goes left (negative) and right (positive). The y-axis goes down (negative) and up (positive).

Translation (Sliding Shapes)

Translation means sliding a shape without rotating or flipping it. Every point moves the same distance in the same direction.

Translate triangle ABC 4 squares right and 2 squares down:

A(1, 5) → A′(5, 3)

B(3, 5) → B′(7, 3)

C(2, 3) → C′(6, 1)

The shape stays exactly the same size and orientation. Only its position changes. Add to the x-coordinate for right (subtract for left) and subtract from the y-coordinate for down (add for up).

Reflection (Mirror Images)

Reflecting a shape means flipping it across a mirror line. Each point in the reflected shape is the same distance from the mirror line as the original, but on the other side.

Reflect point (3, 2) in the y-axis:

The y-axis is the mirror line. 3 is 3 squares to the right of it.

Reflected point: (−3, 2) — 3 squares to the left.

For reflection in the x-axis, the y-coordinate changes sign. For reflection in the y-axis, the x-coordinate changes sign. Count squares carefully — accuracy matters.

SATs-Style Example Question

“A rectangle has three vertices at (1, 2), (1, 6) and (5, 6). What are the coordinates of the fourth vertex?”

The missing vertex must complete the rectangle.

It shares the x-coordinate of (5, 6) → x = 5

It shares the y-coordinate of (1, 2) → y = 2

Answer: (5, 2)

Sketching the points on a quick grid is the fastest way to spot the pattern. Encourage your child to draw whenever coordinates are involved.

Common Mistakes to Watch For

Mixing up x and y — x is always first (along), y is second (up). “Along the corridor, up the stairs.”
Translating in the wrong direction — “3 left” means subtract from x, not add. Read the instruction twice.
Reflecting unevenly — each point must be the same distance from the mirror line. Count squares, don’t eyeball it.
Negative coordinate errors — (−2, −3) is in the bottom-left quadrant. Make sure the signs are correct.

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