1.

Show that the points (a, 0), (0, b) and (3a, – 2b) are collinear.

Answer»

Let the given points be

P(x1, y1) = (a, 0), Q(x2, y2) = (0, b) and

R(x3, y3) = (3a – 2b).

∴ Area of ∆PQR = \(\frac{1}{2}\)|x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|

= \(\frac{1}{2}\)|a(b + 2b) + 0(−2b − 0) + 3a(0 − b)|

= 0

⇒ the points (a, 0), (0, b) and (3a, – 2b) are collinear.


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