Question

Say true or false.

The ratio in which the point $(3,5)$ divides line segment joining the points $(1,3)$ and $(4,6)$ is $2:1$.

• A. True
• B. False

Answer 1

The correct option is A True

Let us consider a point $P(3,5)$ that divides line joining $A(1,3)$ and $B(4,6)$ as per $k:1$ ratio, then the co-ordinates of $P$ is $[\frac{4k+1}{k+1},\frac{6k+3}{k+1}]$.

But we already are given co-ordinates of $P$,

$\therefore \frac{4k+1}{k+1}=3$ and rewriting we have,

$\therefore 4k+1=3k+3$ or $k=2=\frac{2}{1}$

$\therefore$ the point $P(3,5)$ divides line joining $A(1,3)$ and $B(4,6)$ in $2:1$ ratio.