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Analytic Geometry2D

The Straight Line - Theory & Concepts - Analytic Geometry Line Distance Angle

Equations of lines, slopes, intercepts, distances, and angles between lines.

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3.0
4.0
-12.0
4.0
5.0
Calculated Distanced = 4.000
Shortest distance from Point P (4, 5) to line is 4.000Grid lineGrid backgroundHorizontal AxisVertical AxisLine Equation: 3x + 4y + -12 = 0Perpendicular projection vector from P to the linePoint P at (4.0, 5.0)Closest Point Q on line at (1.6, 1.8)
d=∣(3.0)(4.0)+(4.0)(5.0)+(−12.0)∣(3.0)2+(4.0)2=4.000d = \frac{|(3.0)(4.0) + (4.0)(5.0) + (-12.0)|}{\sqrt{(3.0)^2 + (4.0)^2}} = 4.000

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