KEVOS® MAKEOS · Geometry
Straight Lines: Intersection, Angle and Distance
Where do these two lines cross, at what angle, and how far is a point from the first line?
Analytical geometry of straight lines each defined by two points: slopes and intercepts, the intersection point, the angle between the lines, and the perpendicular distance and foot of the perpendicular from a point to the first line.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Line 1 | ||
| x₁ | mm | First point on line 1. |
| y₁ | mm | First point on line 1. |
| x₂ | mm | Second point on line 1. |
| y₂ | mm | Second point on line 1. |
| Line 2 | ||
| x₃ | mm | First point on line 2. |
| y₃ | mm | First point on line 2. |
| x₄ | mm | Second point on line 2. |
| y₄ | mm | Second point on line 2. |
| Point | ||
| Point x | mm | Point whose distance from line 1 is wanted. |
| Point y | mm | Point whose distance from line 1 is wanted. |
Method and formulas
- Each line in the form A x + B y = C from its two points; the intersection solves both (none when parallel).
- Angle between lines from their direction vectors.
- Distance from a point = |A x₀ + B y₀ − C| ÷ √(A² + B²).
- Example: the lines cross at (53.333, 26.667) at 71.565°.
Limitations
- Plane geometry; each line needs two distinct points.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find a theoretical sharp corner from two drawn edges
- Check a CNC contour intersection
- Measure the distance of a hole from an inclined edge
Who it is for
- CNC programmers
- Toolmakers
- Design engineers
What you get
- Intersection point
- Angle between the lines
- Distance from the point to line 1
Interpreting the result
- Use the foot of the perpendicular as the gauging point when inspecting an edge position.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 40–46. Topic reference; no source tables or recommended settings are reproduced.
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