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Coordinate geometry cheat sheet

All 8 formulas on one page. Print it or save it as a PDF; it fits on 2 sides of A4 or Letter.

Distance formula

d = √((x₂ − x₁)² + (y₂ − y₁)²)

$d$ the distance between the two points (never negative)
$x_{1}$ the x-coordinate of the first point
$y_{1}$ the y-coordinate of the first point
$x_{2}$ the x-coordinate of the second point
$y_{2}$ the y-coordinate of the second point

Midpoint formula

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Missing endpoint

x₂ = 2Mₓ − x₁, y₂ = 2M_y − y₁

$M$ the midpoint of segment AB
$M_{x}$ the x-coordinate of the midpoint
$M_{y}$ the y-coordinate of the midpoint
$x_{1}$ the x-coordinate of endpoint A
$y_{1}$ the y-coordinate of endpoint A
$x_{2}$ the x-coordinate of endpoint B
$y_{2}$ the y-coordinate of endpoint B
$B$ in the calculator's second mode, the unknown endpoint found from A and the midpoint

Slope formula

m = (y₂ − y₁)/(x₂ − x₁)

$m$ the slope (gradient): how much y changes for each 1 that x increases
$x_{1}$ x-coordinate of the first point
$y_{1}$ y-coordinate of the first point
$x_{2}$ x-coordinate of the second point
$y_{2}$ y-coordinate of the second point

Slope-intercept form

y = mx + b

$y$ the y-coordinate of a point on the line
$x$ the x-coordinate of that point
$m$ the slope (gradient)
$b$ the y-intercept: the value of y when x = 0 (some courses call it c)

Point-slope form

y − y₁ = m(x − x₁)

$y$ the y-coordinate of any point on the line
$x$ the x-coordinate of that point
$m$ the slope
$x_{1}$ the x-coordinate of the known point
$y_{1}$ the y-coordinate of the known point

Equation of a circle

(x − h)² + (y − k)² = r²

Centre at the origin

x² + y² = r²

General form

x² + y² + Dx + Ey + F = 0

$r$ the radius
$h$ the x-coordinate of the centre
$k$ the y-coordinate of the centre
$x$ the x-coordinate of a point on the circle
$y$ the y-coordinate of a point on the circle

Slopes of perpendicular lines

m₁·m₂ = −1 ⇔ m₂ = −1/(m₁)

Parallel lines

m₂ = m₁

$m_{1}$ the slope of the first line (not 0)
$m_{2}$ the slope of the perpendicular line

Distance from a point to a line

d = (|ax₀ + by₀ + c|)/(√(a² + b²))

$d$ the shortest (perpendicular) distance
$a$ the coefficient of x in the line's equation
$b$ the coefficient of y
$c$ the constant term (with the equation arranged to equal 0)
$x_{0}$ the x-coordinate of the point
$y_{0}$ the y-coordinate of the point

letx.io · Coordinate geometry cheat sheet · 2026-10-31