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Analytic Geometry2D

Introduction to Analytic Geometry - Theory & Concepts - Analytic Geometry Section Formula

Coordinate systems, distance formula, midpoint formula, slope, angle between lines, symmetry, and area of polygons.

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Section Formula Explorer (Line Segment Division)

Parameters

Ratio Factor m2
Ratio Factor n1

Step-by-Step Solver

Governing Formulas
x=mx2+nx1m+nx = \frac{m x_2 + n x_1}{m + n}y=my2+ny1m+ny = \frac{m y_2 + n y_1}{m + n}
Substitution & Result
x=(2)(6)+(1)(−6)2+1=12+−63=2.00x = \frac{(2)(6) + (1)(-6)}{2 + 1} = \frac{12 + -6}{3} = 2.00
y=(2)(4)+(1)(−4)2+1=8+−43=1.33y = \frac{(2)(4) + (1)(-4)}{2 + 1} = \frac{8 + -4}{3} = 1.33
Section Point: Point P divides segment AB in the ratio 2 : 1. The resulting coordinate is P(2.00, 1.33).
-10 to 10Point A (-6, -4)A(-6, -4)Point B (6, 4)B(6, 4)Point P (2.00, 1.33)P(2.0, 1.3)

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