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in Coordinate Geometry by (49.2k points)
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If the points P (12, 8), Q (–2, a) and R (6, 0) are the vertices of a right angled triangle PQR, where ∠R = 90°, the value of a is 

(a) 6 

(b) –2 

(c) –4 

(d) –6

1 Answer

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by (46.2k points)
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Best answer

(a) 6

ΔPQR is rt. ∠d at R 

⇒ PR2 + QR2 = PQ2

⇒ {(6 – 12)2 +(0 – 8)2} +{(6 + 2)2 +(0 – a)2} = {(–2 – 12)2 + (a – 8)2

⇒ (36 + 64) + (64 + a2) = (196 + a2 – 16a + 64) 

⇒ a2 + 164 = a2 – 16a + 260 

⇒ 16a = 260 – 164 = 96 ⇒ a = 6.

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