Question:

Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

Updated On: Nov 4, 2023
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Solution and Explanation

line segment joining A(– 2, 2) and B(2, 8) into four equal parts
From the figure it is observed that points P,Q,R are dividing the line segment in a ratio 1:3,1:1,3:1 respectively,
Coordinates of P=\((\frac{1\times2+3\times(-2)}{1+3},\frac{1\times8+3\times2}{1+3})\)=\((-1,\frac{7}{2})\)
Coordinates of Q= \((\frac{2+(-2)}{2},\frac{2+8}{3+1})=(0,5)\)
Coordinates of R=  \((\frac{3\times2+1\times(-2)}{1+3},\frac{3\times8+1\times2}{3+1})=(1,\frac{13}{2})\)

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Concepts Used:

Coordinate Geometry

Coordinate geometry, also known as analytical geometry or Cartesian geometry, is a branch of mathematics that combines algebraic techniques with the principles of geometry. It provides a way to represent geometric figures and solve problems using algebraic equations and coordinate systems.
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.