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

Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2 : 3.

A) (1, 3)

B) (2, 6)

C) (3, 4)

D) (4, 6)

Correct Answer: A

Solution :

Let the coordinates of a point are (x, y).

We have, \[{{x}_{1}}=-1,\,{{y}_{1}}=7\] ;

\[{{x}_{2}}=4,\,{{y}_{2}}=-3\]

and \[{{m}_{1}}=2,\,{{m}_{2}}=3\]

\[\therefore\] By using section formula,

\[x=\frac{{{m}_{1}}{{x}_{2}}+{{m}_{2}}{{x}_{1}}}{{{m}_{1}}+{{m}_{2}}}\]

\[=\frac{2\left( 4 \right)+3\left( -1 \right)}{2+3}=\frac{8-3}{5}=\frac{5}{5}=1\]

and \[y=\frac{{{m}_{1}}{{y}_{2}}+{{m}_{2}}{{y}_{1}}}{{{m}_{1}}+{{m}_{2}}}=\frac{2\left( -3 \right)+3\left( 7 \right)}{2+3}\]

\[=\frac{-6+21}{5}=\frac{15}{5}=3\]

Hence, coordinates of the point are (1,3).