question_answer

The ratio in which the point P (m, 6) divides the join A (-4, 3) and B (2, 8) is

A) 2:3

B) 1:2

C) 3:2

D) 2:1

Correct Answer: C

Solution :

\[A\left( -4,\,3 \right),\]\[B\left( 2,\,8 \right)\]and \[P\left( m,\,6 \right)\]

Let P divides the join of AB in the ratio of k : 1.

\[\therefore \,\] y-coordinate of \[P=\frac{k\times 8+1\times 3}{k+1}\]

\[\Rightarrow \,\,\,\,6=\frac{8k+3}{k+1}\]

\[\Rightarrow \,\,\,\,6k+6=8k+3\]

\[\Rightarrow \,\,\,2k=3\]

\[\Rightarrow \,\,\,\,k=\frac{3}{2}\]

\[\therefore\] P divides the join of AB in the ratio of 3 : 2.