निर्देशांक ज्यामिति

Question

बिंदुओं के निम्नलिखित युग्मों के बीच की दूरियाँ ज्ञात कीजिए:
(a, b), (– a, – b)

Solution

माना बिंदु A(a, b) और B(-a, -b) है।
A और B के बीच की दूरी
$space space space space space space space AB space equals space square root of open parentheses straight x subscript 2 plus straight x subscript 1 close parentheses squared plus left parenthesis straight y subscript 2 minus straight y subscript 1 right parenthesis squared end root therefore space space AB space equals space square root of open parentheses negative straight a minus straight a close parentheses squared plus left parenthesis negative straight b minus straight b right parenthesis squared end root space space space space space space space space space space space equals space square root of left parenthesis negative 2 straight a right parenthesis squared plus left parenthesis negative 2 straight b right parenthesis squared end root space space space space space space space space space space space equals space square root of 4 straight a squared plus 4 straight b squared end root space space space space space space space space space space space equals space square root of 4 left parenthesis straight a squared plus straight b squared right parenthesis end root space space space space space space space space space space space equals space square root of 4 left parenthesis straight a squared plus straight b squared right parenthesis end root space space space space space space space space space space space equals space 2 square root of straight a squared plus straight b squared end root$

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