Question

Prove that the point a,o ,a,b and 1,1 are collinear if b1/a+1/b=1

Answer 1

Let A(a,0) , b(0,b) and C(1,1) be the collinear points
Let B divide the line segment joining AC in ratio of k:1
Then,by section formula,the coordiantes of B would be given by (k+a / k+l , k/k+1)
However,we already know that the coordinates of B is (0,b)
So equating, 0 = k+a/k+1 i.e k=-a
Also, b = k/k+1
Substituting k = -a , we get
B= -a / -a+1
1/b = a-1/ a
1/b = 1 - 1/a
1/a + 1/b = 1
Hence proved...mark brain if u like