यदि बिंदु (3, 4) और (a, 2) के बीच की दूरी 8 इकाई है, तो a का मान ज्ञात कीजिए। 

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संकल्पना:

माना कि A (x1, y1) और B (x2, y2), XY - तल में दो बिंदु हैं, तो A और B के बीच की दूरी को निम्न द्वारा ज्ञात किया गया है:

 

गणना:

दिया गया है: बिंदु (3, 4) और (a, 2) के बीच की दूरी 8 इकाई है। 

यहाँ, हमें a का मान ज्ञात करना है। 

चूँकि हम जानते हैं कि, दो बिंदु A (x1, y1) और B (x2, y2) के बीच की दूरी को द्वारा ज्ञात किया गया है।

⇒ 

दोनों पक्षों का वर्ग करने पर हमें निम्न प्राप्त होता है

⇒ (a - 3)2 + 4 = 64

⇒ a2 + 9 - 6a - 60 = 0

⇒ a2 - 6a - 51 = 0

⇒ 

अतः विकल्प A सही उत्तर है। 

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