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Geometry · SS 3

Distance between two points

Find the length of a line joining two points (it is Pythagoras on a grid).

  • d = √((x2 − x1)2 + (y2 − y1)2)

What the letters mean

(x1, y1), (x2, y2)
the two points

Worked example

Find the distance between (1, 2) and (4, 6).

  1. Step 1: Differences

    x: 4 − 1 = 3, y: 6 − 2 = 4

  2. Step 2: Pythagoras

    d = √(32 + 42) = √25 = 5

Final answer: 5 units

See it

Play with this picture from the Gradient, Distance and Midpoint lesson.

-6-6-5-5-4-4-3-3-2-2-1-1112233445566xyP(0, 0)

Your task: plot the point (3, -2)

Drag P. Remember: x first (across), then y (up or down).