Prove that the points (a , b), (c , d) and (a - c, b - d) are collinear if ad = bc. Also show that the straight line passing through these points passes through origin.

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Prove that the points (a , b), (c , d) and (a - c, b - d) are collinear if ad = bc. Also show that the straight line passing through these points passes through origin.

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Text solutionVerified

If the given points be A,B,C then as they are collinear therefore slopes of AC and BC are same.

∴ \frac{d}{c} = \frac{b}{a}

a d = b c

.....(1)
Since AC is

y - b = \frac{d}{c} (x - a)

It will pass through (0, 0) if

- b = \frac{d}{c} (- a)

b c = a d

which is true by (1).

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Question Text	Prove that the points (a , b), (c , d) and (a - c, b - d) are collinear if ad = bc. Also show that the straight line passing through these points passes through origin.
Answer Type	Text solution:1
Upvotes	150

Prove that the points (a , b), (c , d) and (a - c, b - d) are collinear if ad = bc. Also show that the straight line passing through these points passes through origin.

Text solutionVerified

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