If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = \(\frac{3}{7}\) AB and P lies on the line segment AB.
Solution and Explanation
The coordinates of point A and B are (-2,-2) and (2,-4) respectively. since AP=\(\frac{3}{7}AB\)
Therefore, AP: PB=3:4
Point P divides the line segment AB in the ratio 3:4
Coordinates of P = \((\frac{3\times2+4\times(-2)}{3+4},\frac{3\times(-4)+4\times(-2)}{3+4})\)
=\((\frac{6-8}{7},\frac{-12-8}{7})\)
=\((-\frac{2}{7},-\frac{20}{7})\)
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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.