Coordinate Geometry Topic Review summary

Key learning points

• Gradient $m=\frac{y_2-y_1}{x_2-x_1}$; parallel share $m$; perpendicular $m_1m_2=-1$.
• Line equations: $y-y_1=m(x-x_1)$, $y=mx+c$, $ax+by+c=0$.
• Distance $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$; midpoint averages coordinates.
• Intersection of lines: solve simultaneous equations.
• Perpendicular bisectors and circle links appear in mixed questions.

Worked example 1 — Gradient

Gradient from $(1,2)$ to $(5,10)$.

Working

$\frac{8}{4}$.

Worked example 2 — Perpendicular

Line perpendicular to $y=3x+1$ through origin.

Working

Negative reciprocal.

Worked example 3 — Gradient m=\y_2-y_1{x_2-x_1}; parallel sha

Gradient $m=\\frac{y_2-y_1}{x_2-x_1}$; parallel share $m$; perpendicular $m_1m_2=-1$.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Line equations: y-y_1=m(x-x_1), y=mx+c, ax

Line equations: $y-y_1=m(x-x_1)$, $y=mx+c$, $ax+by+c=0$.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.