Using the method of slope, show that the following points are collinear : (i) A(4, 8), B(5, 12), C(9, 28)(ii) A(16, – 18), B(3,

Engineering

Mathematics

Introduction to Determinants

Question

Using the method of slope, show that the following points are collinear :

(i) A(4, 8), B(5, 12), C(9, 28)

(ii) A(16, – 18), B(3, – 6), C(– 10, 6)

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(i) Slope of AB

= \frac{12 - 8}{5 - 4} = \frac{4}{1} = 4

Slope of BC

= \frac{28 - 12}{9 - 5} = \frac{16}{4} = 4

Hence AB | | BC, but B is a point of intersect.

Hence A, B, C are collinear.

(ii) Slope of AB

= \frac{- 6 + 18}{3 - 16} = \frac{12}{- 13} = - \frac{12}{13}

Slope of BC

= \frac{6 + 6}{- 10 - 3} = \frac{12}{- 13} = - \frac{12}{13}

Slope of AB = slope of BC

Hence A, B, C are collinear.

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