SSC Sample Paper Mock Test-15 SSC CGL Tear-II Paper-1

In what ratio does the point \[P\,\,(2,-\,\,5)\]divided the line segment joining \[A\,\,(-\,\,3,5)\] and\[B\,\,(4,-\,\,9)\]?

A) 2 : 3

B) 4 : 3

C) 5 : 1

D) 5 : 2

Correct Answer: D

Solution :

Let the required ratio be k : 1.

Then, the point P is \[\left( \frac{4k-3}{k+1},\frac{-\,\,9k+5}{k+1} \right)\]

\[\therefore \] \[\frac{4k-3}{k+1}=2\] and \[\frac{-\,\,9k+5}{k+1}=-\,\,5\]

\[\Rightarrow \] \[4k-3=2k+2\] and \[-9k+5=-\,\,5k-5\]

\[\Rightarrow \] \[2k=5\] and \[4k=10\]\[\Rightarrow \]\[k=\frac{5}{2}\]

Required ratio is\[\frac{5}{2}:1,\]i.e., 5 : 2.