NUST NET Maths · Maths · Analytic geometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Coordinate geometry turns geometry into algebra. Two points give you a distance, a midpoint and a gradient. The gradient m measures the steepness of a line and equals tan θ, where θ is the angle the line makes with the positive x-axis.
A line is fixed by one point and a gradient, so most questions come down to finding m and then using y − y1 = m(x − x1). For a line written as ax + by + c = 0, read the gradient straight off as −a/b.
Parallel lines have equal gradients. Perpendicular lines have gradients that multiply to −1. Three points are collinear when the gradients between them are equal.
Using the parallel-lines distance formula before the two equations have the same x and y coefficients. Multiply or divide one equation first so that a and b match, then compare the constants.
Answer: 3x + 2y − 7 = 0
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