Prove that the points $(- 1, - 1), (2, 3)$ and $(8, 11)$ are collinear.

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Solution

Line: $(y + 1) = \frac{3 + 1}{2 + 1} (x + 1)$

$3 y + 3 = 4 x + 4 \Rightarrow (3 y - 4 x = 1)$

For colinearity, (8,11) must

satisfy above equation.

$∴ 3 (1) - 4 (8) = 33 - 32 = 1 = 1$

$∴ c o l i n e a r$

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A (- 2, 3, 5), B (1, 2, 3)

C (7, 0, - 1)

Using the distance formula, show that the given points are collinear:

(i) (1, -1), (5, 2) and 9, 5 (ii) (6, 9), (0, 1) and (-6, -7)

(iii) (-1, -1), (2, 3) and (8, 11) (iv) (-2, 5), (0, 1) and (2, 3).

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