Find the ratio in which the point P$(3/4,5/12)$ divides the line segments joining the point A$(1/2,3/2)$ and B$(2,-5)$.

Given that,

Points A$(1/2,3/2)$ and B$(2,-5)$

Let’s consider the point P$(3/4,5/12)$ divide the line segment AB in the ratio k:$1$

As, we know that

P$(3/4,5/12)=(2k+1/2)/(k+1),(2k+3/2)/(k+1)$

Therefore, on  equating the abscissa we get

$3/4=(2k+1/2)/(k+1)$

$3(k+1)=4(2k+1/2)$

$3k+3=8k+2$

$5k=1$

$k=1/5$

Hence, the ratio in which the point P$(3/4,5/12)$ divides is $1:5$