Question

If the point (a,0) and (0,b) and (1,1) lie on the same line, prove that 1/a + 1/b=1

Answer 1

x1= a
x2= 0
x3=1
y1=0
y2=b
y3=1
So
x1(y2-y3)+x2(y3-y1)+x3(y1-y2)=0
a(b-1) + 0(1-0) + 1(0-b)=0
ab-a-b=0
ab-b=a
1-1/a=1/b
1=1/a+1/b