Coordinate geometry
Straight lines: gradient, equation, intersections, parallel and perpendicular.
Y12 builds on GCSE: y = mx + c, point-gradient form y − y1 = m(x − x1), and the perpendicular condition m1m2 = −1.
Worked examples
Through (1, 2) and (3, 8): m = 3, line y = 3x − 1.
Perpendicular to y = 2x + 1 through (4, 7): gradient −½, line y = −½x + 9.
Intersection: solve simultaneously.
Frequently asked questions
Distance between two points?
√((x2−x1)² + (y2−y1)²). Pythagoras.
Midpoint?
((x1+x2)/2, (y1+y2)/2). Average of coordinates.