Gradient and Midpoint of a Line Segment
Grade 4Gradient
The gradient of a line measures how steep it is — how much it rises (or falls) for each unit it moves horizontally.
gradient m = (y₂ − y₁) ÷ (x₂ − x₁)
A positive gradient means the line slopes upward left to right. A negative gradient means it slopes downward. A horizontal line has gradient 0; a vertical line has an undefined gradient.
Midpoint
The midpoint of a line segment is the point exactly halfway between the two endpoints. Just average the x-coordinates and average the y-coordinates.
midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Worked example
EXAMPLE
Find the gradient and midpoint of the line joining A(2, 3) and B(8, 11).
Gradient = (11 − 3) ÷ (8 − 2) = 8 ÷ 6 = 4/3. Midpoint = ((2 + 8)/2, (3 + 11)/2) = (5, 7). Gradient = 4/3; midpoint = (5, 7).
Watch the sign
Always subtract in the same order: (y₂ − y₁) ÷ (x₂ − x₁). If you flip the order for one but not the other you get the wrong sign. It doesn't matter which point is "1" and which is "2" as long as you are consistent.
