Question:

Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.

Updated On: Nov 4, 2023
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Solution and Explanation

Let the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by the x-axis be k:1. 
Therefore, the coordinates of the point of division are \((\frac{-4k+1}{k+1},\frac{5k-5}{k+1})\)

We know that the y-coordinate of any point on the x-axis is 0.
Therefore, the x-axis divides it in the ratio 1:1.

Division point = \((\frac{-4(1)+1}{1+1},\frac{5(1)-5}{1+1})=\frac{-4+1}{2},\frac{5-5}{2}=(\frac{-3}{2},0)\)

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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.