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Proe that the points (a,0), (0,b) and (1,1) are collinear if 1/a+1/b=1.

Proe that the points (a,0), (0,b) and (1,1) are collinear if 1/a+1/b=1.

Grade:12

1 Answers

Arun
25750 Points
6 years ago
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

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