Math · 10 calculators
Distance, midpoint, slope, line equations, parallel and perpendicular lines, section formula and circle equations on the coordinate plane.
Coordinate Geometry
Find the distance between two points (x₁, y₁) and (x₂, y₂) with the distance formula, step by step, in 2D or 3D.
d = √((x₂ − x₁)² + (y₂ − y₁)²)
Also called distance formula calculator · coordinate distance calculator
Coordinate Geometry
Find the midpoint of a line segment between two coordinates with the midpoint formula, or find a missing endpoint.
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Also called midpoint formula calculator · midpoint of two points
Coordinate Geometry
Find the slope (gradient) of a line through two points, its angle of inclination, and the line equation y = mx + b.
m = (y₂ − y₁) / (x₂ − x₁)
Also called slope formula · gradient calculator
Coordinate Geometry
Get the equation of a line through two points in slope-intercept, point-slope and standard form.
y − y₁ = m(x − x₁), m = (y₂ − y₁)/(x₂ − x…
Also called equation of a line · two point form
Coordinate Geometry
Write the equation of a line from one point and a slope in point-slope, slope-intercept and standard forms.
y − y₁ = m(x − x₁)
Also called point slope calculator · point slope formula
Coordinate Geometry
Find the equation of the line parallel to y = mx + b that passes through a given point.
m₂ = m₁
Also called parallel line equation · parallel slope
Coordinate Geometry
Find the equation of the line perpendicular to y = mx + b that passes through a given point, using the negative reciprocal slope.
m₁ × m₂ = −1
Also called perpendicular line equation · perpendicular slope
Coordinate Geometry
Find the point dividing the segment between two points in the ratio m:n, internally or externally.
P = ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)…
Also called section formula · internal division
Coordinate Geometry
Write the standard and general form equation of a circle from its center and radius, or from center and a point on it.
(x − h)² + (y − k)² = r²
Also called equation of a circle · circle standard form
Coordinate Geometry
Area of a triangle from the coordinates of its three vertices using the shoelace formula — also tells you if the points are collinear.
A = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ …
Also called area of triangle with coordinates · shoelace formula
| Distance Between Two Points | d = √((x₂ − x₁)² + (y₂ − y₁)²) |
|---|---|
| Midpoint | M = ((x₁ + x₂)/2, (y₁ + y₂)/2) |
| Slope | m = (y₂ − y₁) / (x₂ − x₁) |
| Line Equation | y − y₁ = m(x − x₁), m = (y₂ − y₁)/(x₂ − x₁) |
| Point-Slope Form | y − y₁ = m(x − x₁) |
| Parallel Line | m₂ = m₁ |
| Perpendicular Line | m₁ × m₂ = −1 |
| Section Formula | P = ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)/(m + n)) |
| Circle Equation | (x − h)² + (y − k)² = r² |
| Coordinate Triangle Area | A = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| |
d = √((x₂ − x₁)² + (y₂ − y₁)²). For (2, 3) and (5, 7): √(3² + 4²) = √25 = 5.
Average the x-coordinates and average the y-coordinates. The midpoint of (−2, 4) and (6, 10) is (2, 7).
It is the change in y for each 1-unit increase in x — "rise over run". Positive slopes go up to the right, negative slopes go down, 0 is horizontal and vertical lines have undefined slope.