Find the slope of the line passing through (2, 3) and (4, 7).

2

Slope m = (y₂ − y₁)/(x₂ − x₁) = (7 − 3)/(4 − 2) = 4/2 = 2.

Understanding Coordinate Geometry questions

Coordinate geometry turns shapes into equations, so distances, midpoints and gradients can all be computed from coordinates alone.

How to approach it

1. Plot or at least sketch the points to see the configuration.
2. Use distance = √((x₂−x₁)² + (y₂−y₁)²) and midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).
3. Find gradients to test whether lines are parallel or perpendicular.
4. Substitute a known point back into the line equation to verify.

Common mistakes to avoid

• Reversing the order of coordinates in the gradient formula.
• Forgetting to square the differences in the distance formula.
• Assuming perpendicular lines have equal rather than negative-reciprocal gradients.

Where it appears: Featured in CBSE Class 10–11, IGCSE and IB coordinate geometry topics.