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प्रश्न
If the three points (3, – 1), (a, 3) and (1, – 3) are collinear, find the value of a
उत्तर
The vertices are A(3, – 1), B(a, 3) and C(1, – 3)
Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`
Slope of AB = `(3 + 1)/("a" - 3) = 4/("a" - 3)`
Slope of BC = `(3 + 3)/("a" - 1) = 6/("a" - 1)`
Since the three points are collinear.
Slope of AB = Slope BC
`4/("a" - 3) = 6/("a" - 1)`
6(a – 3) = 4(a – 1)
6a – 18 = 4a – 4
6a – 4a = – 4 + 18
2a = 14
⇒ a = `14/2` = 7
The value of a = 7
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