Triangle Slope Calculator

Calculate the slope, length, and midpoint of all 3 sides of a triangle from vertex coordinates.

Enter Vertex Coordinates

Vertex A
Vertex B
Vertex C

Results

Perimeter
--
units

Step-by-Step Solution

slope = (y2 - y1) / (x2 - x1)

Understanding Triangle Slopes

The slope of a line segment describes its steepness and direction. For a triangle defined by three vertices in the coordinate plane, each side is a line segment with its own slope. Analyzing slopes helps determine if sides are parallel, perpendicular, or at specific angles.

Key Formulas

Slope

The slope measures the rise over run between two points.

m = (y2 - y1) / (x2 - x1)

Length (Distance)

The Euclidean distance between two points using the distance formula.

d = sqrt((x2-x1)^2 + (y2-y1)^2)

Midpoint

The point exactly halfway between two endpoints.

M = ((x1+x2)/2, (y1+y2)/2)

Special Slope Relationships

Parallel Sides

Two sides are parallel if they have the same slope. In a triangle, no two sides can be parallel (otherwise the figure would not close), but slopes close to each other indicate sides that are nearly parallel.

Perpendicular Sides

Two sides are perpendicular if the product of their slopes equals -1 (or one is horizontal and the other is vertical). A right triangle has exactly one pair of perpendicular sides.

Horizontal and Vertical Sides

A horizontal side has a slope of 0 (no rise). A vertical side has an undefined slope (no run). The calculator identifies these special cases automatically.

Applications

  • Determine if a triangle is a right triangle by checking for perpendicular slopes.
  • Find the equation of each side using point-slope form.
  • Calculate the area using the coordinate geometry (Shoelace formula).
  • Identify the type of triangle (scalene, isosceles, equilateral) from side lengths.
  • Find altitudes, medians, and other triangle features from vertex coordinates.