Question

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

Let A (a, 0), B (0, b), C(1, 1)

1 / a + 1 / b = 1

a + b = ab

ab - b = a

b(a - 1) = a

b = a / (a - 1)

If the Slope of AC = Slope of BC, then A, C, B are collinear.

Slope of AC = 1 / (1 - a)

Slope of BC = (1 - b) / 1

Substituting value of b,

Slope of BC = 1 - (a / (a - 1)

                     = (a - 1 - a) / (a - 1)

                     = -1 / (a - 1)

                     = 1 / (1 - a)

Slope of BC  = Slope of AC

Hence Proved!

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