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

The coordinates of the point, dividing the join of the points \[(5,0)\] and \[(0,4)\] in the ratio \[2:3\] internally, are:

A) \[\left( 3,\frac{8}{5} \right)\]

B) \[\left( 1,\frac{4}{5} \right)\]

C) \[\left( \frac{5}{2},\frac{3}{4} \right)\]

D) \[\left( 2,\frac{12}{5} \right)\]

Correct Answer: A

Solution :

[a] Let the points \[P(x,y)\] divides the join of \[A(5,0)\]and \[B(0,4)\]in the ratio \[2:3\] internally.

\[\therefore \,\,\,x=\frac{2(0)+3(5)}{2+3}=3\] and \[y=\frac{2(4)+3(0)}{2+3}=\frac{8}{5}\]

Hence, the required points is \[\left( 3,\frac{8}{5} \right)\]