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# If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that ah+bk = 1 - Mathematics and Statistics

Sum

If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that "a"/"h" + "b"/"k" = 1

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#### Solution

A (h, 0), B (0, k) and C (a, b) lie on a line.

∴ A, B, Care collinear.

∴ slope of AB = slope of BC

∴ ("k" - 0)/(0 - "h") = ("b" - "k")/("a" - 0)

∴ - "k"/"h" = ("b" - "k")/"a"

∴ – ak = bh – hk

∴ ak + bh = hk

∴ ("ak" + "bh")/"hk" = 1

∴ "a"/"h" + "b"/"k" = 1

which is the required condition.

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