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