10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

In what ratio does the point \[P(3,4)\] divided the line segment joining the points \[A(1,2)\] and \[B(6,7)\] ?

A) \[1:2\]

B) \[2:3\]

C) \[3:4\]

D) \[1:1\]

Correct Answer: B

Solution :

[b] Let \[P(3,4)\] divide the join of \[A(1,2)\] and \[B(6,7)\] in the ratio \[k:1\].

\[\therefore \] Coordinates of P are \[\frac{6k+1}{k+1}=3\,\,\,\,\,\Rightarrow \,\,k=\frac{2}{3}\]

and \[\frac{7k+2}{k+1}=4\,\,\,\,\Rightarrow \,\,\,k=\frac{2}{3}\]

\[\therefore \]The required ratio is \[\frac{2}{3}:1\] i.e., \[2:3\]