[Solved] If The Points With Coordinates (-5, 0), (5p2, 10p) And (5q2,

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Concept:

1). The area of the triangle formed by three vertices that are collinear is zero.

2). Area of a triangle formed by (x1,y1), (x2,y2), and (x3,y3) is given by,

Area = \(\displaystyle \frac{1}{2}\)[x1(y2 - y3) + x2(y3 − y1) + x3(y1 − y2)]

Calculation:

Given,

Points with coordinates (-5, 0), (5p2, 10p) and (5q2, 10q) are collinear

∴ Area of △ABC=0

We know that,

Area of a triangle formed by (x1,y1), (x2,y2), and (x3,y3) is given by,

Area = \(\displaystyle \frac{1}{2}\)[x1(y2 - y3) + x2(y3 − y1) + x3(y1 − y2)]

∴ Area of △ABC = \(\displaystyle \frac{1}{2}\)[-5(10p − 10q) + 5p2(10q − 0) + 5q2(0 − 10p)]

⇒ 0 = -50p + 50q + 50p2q - 50q2p

⇒ 0 = 50(q - p) + 50(p2q - q2p)

⇒ 50(p - q) = 50(p2q - q2p)

(p - q) = (p2q - q2p)

(p - q) = pq(p - q)

⇒ pq = 1 [p ≠ q]

∴ The value of pq = 1

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