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By Using the Concept of Equation of a Line, Prove that the Three Points (3, 0), (–2, –2) and (8, 2) Are Collinear. - Mathematics

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Question

By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.

Solution

In order to show that points (3, 0), (–2, –2), and (8, 2) are collinear, it suffices to show that the line passing through points (3, 0) and (–2, –2) also passes through point (8, 2).

The equation of the line passing through points (3, 0) and (–2, –2) is

It is observed that at x = 8 and y = 2,

L.H.S. = 2 × 8 – 5 × 2 = 16 – 10 = 6 = R.H.S.

Therefore, the line passing through points (3, 0) and (–2, –2) also passes through point (8, 2). Hence, points (3, 0), (–2, –2), and (8, 2) are collinear.

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By Using the Concept of Equation of a Line, Prove that the Three Points (3, 0), (–2, –2) and (8, 2) Are Collinear. Concept: Various Forms of the Equation of a Line.
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