Question

{x,y} is any point on the line joining the points {a,0} and {0,b}. PROVE THAT : X/A +Y/B = 1 Plz answer fast

Answer 1

( a , 0) , ( 0, b ) and (x , y) are colinear points .e.g these points passing through a linear equation , so slope forming by all points will be equal .

hence,

slope =( b -0)/( 0 -a) =( y -0 )/(x -a)

b/ -a = y/(x - a)

bx -ab = -ay

bx + ay = ab

divide both side by ab

bx/ab + ay/ab = ab/ab

x/a + y/b = 1

hence proved

2nd method ;-
if all three points are colinear then area of ∆ form by these points equals zero

e.g ar ∆ =1/2{a(b-y) +0 +x(0-b)}

0 = ab -ay -bx

bx + ay = ab

hence ,
x/a +y/b = 1

hence proved