Question

1. The line segment joining the point \( (1,2) \) and \( (a, b) \) is divided by line \( 3 x+4 y \) \( =7 \) in ratio \( 4: 9 \), then \( (a, b) \) is

Answer 1

P(1,2) and Q(a,b)   line joining PQ divides the line 3x+4y =7 in 4:9 ration.

let M be a point which divides PQ in 4:9

M ( (4a+9)/13  , (4b+18)/13 )

M lies on 3x+4y =7   .. then

3(  4a+9)/13 ) + 4 ((4b+18)/13) = 7

12a + 27 + 16b + 72 = 91

3a + 4b = - 2

There are several point which satisfy the above condition

for example , if b =1 then a = -2   so ( -2,1) one the points

if b = 7 then a = -10 so ( -10, 7 ) is another point.