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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
Equation of the line passing through the points A(3, 0), B(−2, –2)
y − y1 = `("y"_2 - "y"_1)/("x"_2 - "x"_1) ("x" - "x"_1)`
y − 0 = `(-2 -0)/(-2 -3) ("x" - 3)`
or y = `2/5 ("x" - 3)`
or 5y = 2x − 6
⇒ 2x − 5y − 6 = 0
If the point C(8, 2) falls on this line then its coordinates will satisfy this equation.
∴ 2 × 8 – 5 × 2 – 6 = 0
or 16 – 16 = 0
Hence, the given points A, B, C are collinear.
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