Q44 of 77 Page 7


If the points (1, 4), (r, -2) and (-3, 16) are collinear, find r.

r = 3
SOLUTION:

The condition for collinearity of three given points (x 1 , y 1 ), (x 2 , y 2 ) and (x 3 , y 3 ) is
x 1 (y 2 - y 3 ) + x 2 (y 3 - y 1 ) + x 3 (y 1 - y 2 ) = 0.
⇒ 1× (-2 - 16) + r× (16 - 4) + (-3) × (4 - (-2)) = 0
⇒ (-18) + r× (12) -3× (6) = 0
⇒ -18 + 12r – 18 = 0

⇒ 12r = 36
∴ r = 3.

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