co-ordinategeometry

let the line ax+by=ab meet the x and y axes in A and B respectively.

We see that it intersects the x axis in (a,0)... [substutue y=0 in the equationof theline and you get this point.]

 and

 the y axis in (0,b)....[ pt x=0 in the equation of the line to get this point]

Let O be the origin

So the distance OA= a units

 and

OB= b units.

in right  triangle OAB,

arera of OAB=

(1/2)*(base)*(altitude)=(1/2)(a)(b)=ab/2