Question

find the ratio in which the line 2x+3y=10 divides the line segment joining the points (1,2) and (2,3)

Answer 1

attached diagram,
we know that ⊥ distance, d of P(x₁,y₁) from ax+by+c=0 is 
d= |ax₁+by₁+c|/√(a²+b²)

∴ lets find the ⊥ distance of A,B from 2x+3y=10
if d₁/d₂ = |ax₁+by₁+c|/|ax₂+by₂+c| = |2×1+3×2-10|/|2×2+3×3-10| = |-2/3|

applying properties of similar triagles 
 we get that the ratio is 2/3