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in Coordinate Geometry by (24.0k points)
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If the points A(1, 2), B(2, 4) and C(3, a) are collinear, what is the length of BC ?

(a) √2 units 

(b) √3 units 

(c) √5 units 

(d) 5 units

1 Answer

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Best answer

(c) √5 units 

Area of Δ ABC = 0 for collinearity of A, B, C.

⇒ \(\frac{1}{2}\)[1(4 – a) + 2(a – 2) + 3(2 – 4)] = 0 

⇒ 4 – a + 2a – 4 + 6 – 12 = 0 

⇒ a – 6 = 0 ⇒ a = 6. 

∴ Point C ≡ (3, 6)

⇒ BC = \(\sqrt{(3-2)^2+(6-4)^2}\) = \(\sqrt{1+4}\) = √5 units .

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