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Question

If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: ah+bk=1.

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Solution

The given points are A (h, 0), P (a, b) and B (0, k).
Thus, we have,

Slope of AP=b-0a-hSlope of BP=b-ka-0

For the given points to be collinear, we must have,

Slope of AP = Slope of BP

b-0a-h=b-ka-0ba-h=b-kaab=ab-ak-bh+hkak+bh=hkah+bk=1 On dividing both sides by hk

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