Coordinate Geometry
Midpoint Formula
Find the midpoint of two 2D points.
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
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Coordinate Geometry
Calculate slopes, midpoints, line equations, and distances on two- and three-dimensional coordinate planes.
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Coordinate Geometry
Slope Finder
Find slope from two points.
m = (y₂ − y₁) / (x₂ − x₁)
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Coordinate Geometry
Distance of Two Points
Find 2D distance.
d = √((x₂ − x₁)² + (y₂ − y₁)²)
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Coordinate Geometry
Point-to-Line Distance
Distance from a point to Ax+By+C=0.
d = |Ax₀ + By₀ + C| / √(A² + B²)
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Coordinate Geometry
Circle Equation Maker
Build a circle equation from center and radius.
(x − h)² + (y − k)² = r²
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Coordinate Geometry
Point and Circle
Classify a point as inside, on, or outside.
(x − h)² + (y − k)² compared with r²
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Coordinate Geometry
Graph Horizontal Offset
Rewrite y=f(x−h)+k and explain its graph shift.
y = f(x − h) + k
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Coordinate Geometry
3D Distance Formula
Distance between two 3D points.
d = √((Δx)² + (Δy)² + (Δz)²)
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Coordinate Geometry
Test for Collinear Points
Use a cross product to test three points.
(x₂−x₁)(y₃−y₁) − (y₂−y₁)(x₃−x₁) = 0
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Coordinate Geometry
3D Midpoint Finder
Midpoint between two 3D points.
M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)
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Coordinate Geometry
Sphere Equation Maker
Build a sphere equation.
(x−h)² + (y−k)² + (z−ℓ)² = r²
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Coordinate Geometry
Two Points → Line Equation
Create line equations from two points.
m = (y₂−y₁)/(x₂−x₁); y−y₁=m(x−x₁)
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Coordinate Geometry
Distance of Parallel Lines
Distance between parallel standard-form lines.
d = |C₂ − C₁| / √(A² + B²)
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