Question

The ratio in which perpendicular through (4,1) divides the line joining (2,-1) (6,5) is

Answer 1

Substitute the values x₁=2,x₂=6,y₁=-1and y₂=5 and (x,y) =(4,1) in section formula .
(x,y) = (x₁m₂+x₂m₁/m₁+m₂,y₁m₂+y₂m₁/m₁+m₂) where m₁:m₂ is the required ratio.

(4,1)=(2m₂₊6m₁/m₁₊m₂,5m₁-m₂/m₁₊m₂) 

2m₂₊6m₁/m₁₊m₂=4
2m₂+6m₁=4m₁+4m₂

4m₁-2m₁=6m₂-4m₂
2m₁=2m₂
m₁/m₂=2/2
m₁/m₂=1

Therefore m₁:m₂=1:1

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