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.
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.
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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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.