equation of the line whose portion intercepted between the axes is divided by the point (3,4) in
the ratio 1:2
Answers
Given : line whose portion intercepted between the axes is divided by the point (3,4) in the ratio 1:2
To find : Equation of line
Solution:
Let say Points on axis are
( x , 0 ) & ( 0 , y )
point ( 3 , 4) divide ( x , 0 ) & ( 0 , y ) in ratio 1 : 2
=> 3 = ( 1 * 0 + 2x)/3
=> 9 = 2x
=> x = 9/2
4 = (1 * y + 2 * 0)/3
=> y = 12
Points are
( 9/2 , 0) & ( 0 , 12)
Slope = 12 /(-9/2) = -8/3
y - 12 = (-8/3)(x - 0)
=> 3y - 36 = -8x
=> 8x + 3y = 36
or if point ( 3 , 4) ( 0 , y ) & ( x , 0 ) divide in ratio 1 : 2
=> 3 = ( 1 * x + 2* 0)/3 => x = 9
4 = ( 1 * 0 + 2y)/3 => y = 6
( 0 , 6) & (9, 0) are points
slope = -6/9 = -2/3
y - 6 = -(2/3)(x - 0)
=> 3y - 18 = -2x
=> 2x + 3y = 18
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