Question

Find the ratio in which the point (2,1) divides the join of the points (1,-2) and (4,7)

Answer 1

let the point A(1,-2) and B(4,7)
point c(2,1) divide the joining of line AB
suppose C divided in line AB in the ratio k:1
then,
x=(kx2 + x1)÷(k+1)
y=(ky2+y1)÷(k+1)

now ,

$2 = \frac{k4 + ( - 2)}{4 + 1}$
4k-2=10
k=12/4
k=3/1
hence point C divide the line in the ratio of 3:1