Question
Download Solution PDFयदि बिंदु P(-2, 1), Q(α, β) और R(4, -1) संरेख हैं और α - β = -3 है, तो (α + β) का मान है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
बिंदु: P(-2, 1), Q(α, β), R(4, -1)
α - β = -3
प्रयुक्त सूत्र:
संरेख बिंदुओं के लिए, PQ की प्रवणता = QR की प्रवणता
प्रवणता सूत्र: (y2 - y1) / (x2 - x1)
गणना:
PQ की प्रवणता = (β - 1) / (α + 2)
QR की प्रवणता = (-1 - β) / (4 - α)
चूँकि P, Q, R संरेख हैं:
⇒ (β - 1) / (α + 2) = (-1 - β) / (4 - α)
वज्र गुणा करने पर:
⇒ (β - 1)(4 - α) = (-1 - β)(α + 2)
⇒ 4β - βα - 4 + α = -α -2 - βα - 2β
⇒ 4β + α + α + 2β = -2 + 4
⇒ 6β + 2α = 2
⇒ 3β + α = 1
दिया गया है कि α - β = -3:
α - β = -3 से ⇒ α = β - 3
3β + α = 1 में प्रतिस्थापित कीजिए:
⇒ 3β + (β - 3) = 1
⇒ 4β - 3 = 1
⇒ 4β = 4
⇒ β = 1
इसलिए, α = 1 - 3 = -2
α + β = -2 + 1 = -1
∴ सही उत्तर -1 है।
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