Question

What is the ratio in which $P(2,5)$ divides the line joining the points $(8,2)$ and $(-6,9)$?

• A. $3:4$
• B. $1:3$
• C. $4:3$
• D. $1:4$

Answer 1

The correct option is A $3:4$

Given: The points $A(8,2)$ and $B(-6,9)$.

Let $P(2,5)$ divides the line joining the give points in ratio $k:1=m:n$.

By section formula,

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

We have,

$(2,5)=(\frac{-6k+8}{k+1},\frac{9k+2}{k+1})$

Equating the $x$ coordinates,

$\Rightarrow \frac{-6k+8}{k+1}=2$

$-6k+8=2k+2$

$-8k=-6\Rightarrow k=\frac{3}{4}$

$\therefore$ The ratio $=3:4=k:1$