Revision notes
Find how steep a line is, how far apart two points are, and the point halfway between — WASSCE essentials.
Roads bend, but a map app can still tell you the straight-line distance between two places — and where the halfway point is to meet a friend. It does it with coordinates and three simple formulas you're about to master.
A point is written (x, y): go x across, then y up (or down if negative).
The gradient tells you how steep a line is: gradient = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁).
Positive gradient: the line goes uphill (left to right). Negative: downhill. Zero: flat.
🔑 Key idea: Gradient m = (y₂ − y₁) / (x₂ − x₁)
Gradient of A(1, 2) and B(5, 10)
Step 1: Change in y (rise)
y₂ − y₁ = 10 − 2 = 8
Step 2: Change in x (run)
x₂ − x₁ = 5 − 1 = 4
Step 3: Divide rise by run
m = 84 = 2
Why? Positive gradient: the line goes UP from left to right.
Answer: m = 2
Distance uses Pythagoras: the rise and run are two sides of a right-angled triangle, and AB is the longest side. d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Midpoint is the average of the two points: M = ( (x₁ + x₂) ÷ 2 , (y₁ + y₂) ÷ 2 )
🔑 Key idea: Distance = Pythagoras. Midpoint = average.
Distance between A(1, 1) and B(4, 5)
Step 1: Find the horizontal and vertical gaps
x₂ − x₁ = 4 − 1 = 3
y₂ − y₁ = 5 − 1 = 4
Step 2: Square and add (Pythagoras)
3² + 4² = 9 + 16 = 25
Step 3: Take the square root
√25 = 5
Answer: 5 units
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.