Question

Find the ratio in which $(2,1)$ divides the line segment joining $(1,4),(4,-5)$

Answer 1

Let $P(x,y)=(2,1)$

$A(x_1,y_1)=(1,4),B(x_2,y_2)=(4,-5)$ be the points of a line segment.

$\therefore$ the required ratio is

$x_1-x:x-x_2=1-2:2-4=-1:-2=1:2$

and

$y_1-y:y-y_2=2-1:1-(-1)=1:2$