Coordinate Geometry Calculator

Coordinate Geometry is evaluated from Line 1 - Point 1, Line 1 - Point 1 and Line 1 - Point 2. The calculation reports Distance, Midpoint and Slope.

Results

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About the Coordinate Geometry Calculator

Coordinate Geometry is treated here as a quantitative relation between Line 1 - Point 1, Line 1 - Point 1, Line 1 - Point 2 and Line 1 - Point 2 and Distance, Midpoint, Slope and Equation: y=mx+b.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
m = (y₂ - y₁)/(x₂ - x₁)
Line: y = mx + b
Angle: θ = arctan(|(m₂ - m₁)/(1+m₁m₂)|)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

m = (y₂ - y₁)/(x₂ - x₁)
Line: y = mx + b
Angle: θ = arctan(|(m₂ - m₁)/(1+m₁m₂)|)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Two Perpendicular Roads

Inputs

x1: 0 y1: 0 x2: 4 y2: 8 x3: 0 y3: 6 x4: 8 y4: 2
Distance: 8.944272 units. Midpoint: (2, 4). Slope: 2. Equation: y=mx+b: y = 2x + 0. Slope: -0.5. Angle Between Lines: 90 deg. Lines Relationship: Perpendicular

With Line 1 - Point 1 = 0, Line 1 - Point 1 = 0, Line 1 - Point 2 = 4 and Line 1 - Point 2 = 8 as the stated inputs, the result is Distance = 8.944272 units, Midpoint = (2, 4) and Slope = 2. Each value corresponds to the declared output fields.

Example 2: Parallel Highway Lanes

Inputs

x1: 0 y1: 0 x2: 10 y2: 5 x3: 0 y3: 12 x4: 10 y4: 17
Distance: 11.18034 units. Midpoint: (5, 2.5). Slope: 0.5. Equation: y=mx+b: y = 0.5x + 0. Slope: 0.5. Angle Between Lines: 0 deg. Lines Relationship: Parallel

With Line 1 - Point 1 = 0, Line 1 - Point 1 = 0, Line 1 - Point 2 = 10 and Line 1 - Point 2 = 5 as the stated inputs, the result is Distance = 11.18034 units, Midpoint = (5, 2.5) and Slope = 0.5. Each value corresponds to the declared output fields.

Example 3: Intersection Point of Two Streets

Inputs

x1: 0 y1: 1 x2: 4 y2: 5 x3: 0 y3: 7 x4: 4 y4: 3
Distance: 5.656854 units. Midpoint: (2, 3). Slope: 1. Equation: y=mx+b: y = 1x + 1. Slope: -1. Angle Between Lines: 90 deg. Lines Relationship: Perpendicular

With Line 1 - Point 1 = 0, Line 1 - Point 1 = 1, Line 1 - Point 2 = 4 and Line 1 - Point 2 = 5 as the stated inputs, the result is Distance = 5.656854 units, Midpoint = (2, 3) and Slope = 1. Each value corresponds to the declared output fields.

Example 4: Surveying — Property Corner

Inputs

x1: 100 y1: 200 x2: 400 y2: 350
Distance: 335.410197 units. Midpoint: (250, 275). Slope: 0.5. Equation: y=mx+b: y = 0.5x + 150. Slope: 0. Angle Between Lines: 0 deg. Lines Relationship: Intersecting

With Line 1 - Point 1 = 100, Line 1 - Point 1 = 200, Line 1 - Point 2 = 400 and Line 1 - Point 2 = 350 as the stated inputs, the result is Distance = 335.410197 units, Midpoint = (250, 275) and Slope = 0.5. Each value corresponds to the declared output fields.

Common Use Cases

  • Find all properties of a line from two points
  • Calculate angle between two intersecting lines
  • Determine point of intersection of two lines
  • Find equation of perpendicular or parallel line