Pythagoras on a Coordinate Grid
Grade 5Distance between two points
When you have two points on a grid, the horizontal and vertical distances between them form the two shorter sides of a right-angled triangle. The straight-line distance between the points is the hypotenuse.
distance = √((x₂ − x₁)² + (y₂ − y₁)²)
How to set it up
Find the horizontal distance: subtract the x-coordinates (ignore any negative sign — you are measuring a length). Find the vertical distance: subtract the y-coordinates. Then apply Pythagoras.
You do not need to memorise the distance formula separately. Just find the horizontal and vertical gaps, then use a² + b² = c². Same idea, just applied to coordinates.
Worked example
EXAMPLE
Find the distance between points A(1, 2) and B(7, 10).
Horizontal gap = 7 − 1 = 6. Vertical gap = 10 − 2 = 8. Distance² = 6² + 8² = 36 + 64 = 100. Distance = √100 = 10 units.
