Perpendicular lines: why $m_1 m_2 = -1$ isn't enough

Published 2026-03-18 · Written by Pete Bromfield

Perpendicular-line questions have shown up on every Edexcel Paper 1 since 2018. They're a guaranteed 3-4 marks — and yet students still fumble one of the sub-marks. Here's the map.

The rule

Two lines are perpendicular iff $m_1 \cdot m_2 = -1$. That means: flip the fraction, flip the sign.

Worked example

Line $\ell_1$ has equation $y = 2x + 5$. Line $\ell_2$ is perpendicular to $\ell_1$ and passes through $(4, -1)$. Find the equation of $\ell_2$.

1. M1 — Identify $m_1 = 2$, so $m_2 = -\tfrac{1}{2}$.
2. M1 — Use $y - y_0 = m(x - x_0)$ with $(4, -1)$: $y + 1 = -\tfrac{1}{2}(x - 4)$.
3. A1 — Simplify to $y = -\tfrac{1}{2}x + 1$.

The 1-mark trap in the "show that" version

When the question says "show that $\ell_2$ passes through the point $(0, 1)$", you need to substitute $(0, 1)$ into your equation and demonstrate LHS = RHS. Writing just "yes it does" gets zero marks. Show the substitution.

Drill

10 perpendicular-line questions on Skills Practice tags → Coordinate Geometry. Try them non-calculator.