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

Line formed by joining \[(-1,1)\] and \[(5,7)\] is divided by a Line \[\text{x}+\text{y}=\text{4}\]in the ratio of:

A) \[1:2\]

B) \[1:3\]

C) \[3:4\]

D) \[1:4\]

Correct Answer: A

Solution :

[a] Let line \[x+y=4\] divides the line joining the points \[(-1,1)\]and \[(5,7)\]at C in the ratio \[k:1\].

\[\therefore \] Coodinates of C are \[\left( \frac{5k-1}{k+1},\,\,\frac{7k+1}{k+1} \right)\]

C lies on the line \[x+y=4\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{5k-1}{k+1}+\frac{7k+1}{k+1}=4\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,k=\frac{1}{2}.\]

Hence, ratio \[1:2\].