Relation between x and y, if the points (x, y), (1, 2) and (7, 0) are collinear is ____

Engineering

Mathematics

Introduction to Determinants

Question

Relation between x and y, if the points (x, y), (1, 2) and (7, 0) are collinear is _____

x + 3y = 7

x + 3y = 14

– x + 3y = 7

– x + 3y = 14

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For the points AB = (x, y), BC = (1, 2) and CD = (7, 0) to be collinear they must have area = 0.

Thus, area of a triangle ABC = $\frac{1}{2} (x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})) = 0$

$= \frac{1}{2} (2 x \times 2 + 6 y - 14) = 0$

= (2x + 6y – 14) = 0

Thus, we have the relation x + 3y = 7 for the points to be collinear.

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