Cambridge Primary Checkpoint 0845 · Topic 8 of 10

Position, direction and transformations

Using coordinates in all four quadrants, compass directions and turns, and reflecting, translating and rotating shapes.

📌 Key points

Coordinates are written (x, y). Go along the x-axis first, then up or down the y-axis: "along the corridor, then up the stairs".
The origin is the point (0, 0), where the x-axis and the y-axis cross.
The axes split the grid into four quadrants. Points left of the y-axis have a negative x; points below the x-axis have a negative y.
A reflection flips a shape in a mirror line. Each point ends up the same distance from the line, on the other side.
Reflecting in the x-axis changes the sign of the y-coordinate: (3, 2) goes to (3, −2). Reflecting in the y-axis changes the sign of x.
A translation slides a shape without turning it, e.g. 3 squares right and 2 squares down.
A rotation turns a shape about a point (the centre of rotation), e.g. 90° clockwise or 180°.
After a reflection, translation or rotation, the shape is still exactly the same size and shape.
A quarter turn is 90°, a half turn is 180° and a full turn is 360°. Clockwise from North: North, East, South, West.

Coordinates: A pair of numbers (x, y) that give the position of a point on a grid.
Origin: The point (0, 0) where the axes cross.
Quadrant: One of the four parts a grid is split into by the x-axis and y-axis.
Reflection: Flipping a shape over a mirror line.
Translation: Sliding a shape in a straight line, without turning it.
Rotation: Turning a shape about a fixed point.
Congruent: Exactly the same shape and size.

The point A (2, 5) is translated 4 squares left and 6 squares down. What are the new coordinates?

Left and right change the x-coordinate: 2 − 4 = −2.
Up and down change the y-coordinate: 5 − 6 = −1.
The new point is (−2, −1).
Both coordinates are negative, so the point is in the bottom-left quadrant. Answer: (−2, −1).

💡 Test tip

Always read the x-coordinate first, and check the signs: left of the origin or below it means negative.

Test yourself8 questions from a bank of 22. A new mix every time.