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निर्देशांक ज्यामिति

Question

Wired Faculty App

निम्नलिखित बिंदुओं द्वारा बनने वाले चतुर्भुज का प्रकार (यदि कोई है तो) बताइए तथा अपने उत्तर के लिए कारण भी दीजिए:
(4, 5), (7, 6), (4, 3), (1, 2)

Solution

माना A(4, 5), B(7, 6), C(4, 3) D(1, 2)

space space space space space space AB space equals space square root of open parentheses 7 minus 4 close parentheses squared plus left parenthesis 6 minus 5 right parenthesis squared end root rightwards double arrow space space space AB space equals square root of open parentheses 3 close parentheses squared plus left parenthesis 1 right parenthesis squared end root equals square root of 9 plus 1 end root equals square root of 10 space space space space space space BC space equals square root of open parentheses 4 minus 7 close parentheses squared plus left parenthesis 3 minus 6 right parenthesis squared end root rightwards double arrow space space BC space equals space square root of open parentheses negative 3 close parentheses squared plus left parenthesis negative 3 right parenthesis squared end root rightwards double arrow space space space BC space equals space square root of 9 plus 9 end root equals square root of 18 space space space space space space CD space equals space square root of left parenthesis 1 minus 4 right parenthesis squared plus left parenthesis 2 minus 3 right parenthesis squared end root rightwards double arrow space space CD space space equals space square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared end root rightwards double arrow space space space CD space equals space square root of 9 plus 1 end root equals square root of 10 space space space space space space space DA space equals square root of left parenthesis 4 minus 1 right parenthesis squared plus left parenthesis 5 minus 2 right parenthesis squared end root rightwards double arrow space space space DA space equals space square root of left parenthesis 3 right parenthesis squared plus left parenthesis 3 right parenthesis squared end root rightwards double arrow space space space DA space equals space square root of 9 plus 9 end root equals square root of 18 space space space

AB space equals space CD space equals space square root of 10 BC space equals space DA space equals space square root of 18

rightwards double arrow

चतुर्भुज की सामने की भुजाएँ समान है

space space space space space space space space space AC space equals space square root of left parenthesis 4 minus 4 right parenthesis squared plus left parenthesis 3 minus 5 right parenthesis squared end root rightwards double arrow space space space space space AC space equals space square root of 0 plus left parenthesis negative 2 right parenthesis squared end root rightwards double arrow space space space space space AC space equals space square root of 0 plus 4 end root equals square root of 4 equals 2 space space space space space space space space BD space equals space square root of open parentheses 1 minus 7 close parentheses squared plus left parenthesis 2 minus 6 right parenthesis squared end root rightwards double arrow space space space space BD space space equals space square root of left parenthesis negative 6 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared end root rightwards double arrow space space space space BD space space equals space space square root of 36 plus 16 end root equals square root of 52

यहाँ AB=CD, BC=DA
चतुर्भुज जिसकी भुजाएँ बराबर हैं। सम्मुख भुजाएँ बराबर हैं। चतुर्भुज एक समांतर चतुर्भुज है।

Some More Questions From निर्देशांक ज्यामिति Chapter

y का वह मान ज्ञात कीजिए, जिसके लिए बिंदु P(2, -3) और Q(10, y) के बीच की दूरी 10 मात्रक है।

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