question_answer

If a TC at the point I, lying on the straight line joining Q and R such that it divides the distance between them in the ratio of 1 : 2. Then coordinates of I are

A) \[\left( \frac{22}{3},\,\frac{11}{3} \right)\]

B) \[\left( \frac{28}{3},\,\frac{14}{3} \right)\]

C) \[\left( 6,\,1 \right)\]

D) \[\left( 9,\,1 \right)\]

Correct Answer: B

Solution :

Let the coordinates of I be (x, y)

By section formula,

\[x=\frac{1\times 10+2\times 9}{1+2}=\frac{10+18}{3}=\frac{28}{3}\]

\[y=\frac{1\times 6+2\times 4}{1+2}=\frac{6+8}{3}=\frac{14}{3}\]

Hence, the coordinates of I is

\[\left( \frac{28}{3},\,\frac{14}{3} \right)\]