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निर्देशांक ज्यामिति

Question
CBSEHHIMAH10010037

निम्नलिखित बिंदुओं द्वारा बनने वाले चतुर्भुज का प्रकार (यदि कोई है तो) बताइए तथा अपने उत्तर के लिए कारण भी दीजिए:
(–3, 5), (3, 1), (0, 3), (–1, – 4)

Solution

माना A=(–3, 5), B=(3, 1), C=(0, 3), D=(–1, – 4)
AB space equals space square root of left parenthesis negative 3 minus 3 right parenthesis squared plus left parenthesis 5 minus 1 right parenthesis squared end root
space space space space space equals space square root of left parenthesis negative 6 right parenthesis squared plus 4 squared end root space equals space square root of 36 space plus space 16 end root space equals space square root of 52 space equals space 2 square root of 13
BC space equals space square root of left parenthesis 3 plus 0 right parenthesis squared plus left parenthesis 1 minus 3 right parenthesis squared end root
space space space space space equals space square root of 9 plus left parenthesis negative 2 right parenthesis squared end root space equals space square root of 9 space plus space 4 end root space equals space square root of 13
CD space equals space square root of left parenthesis 0 plus 1 right parenthesis squared plus left parenthesis 3 minus left parenthesis negative 4 right parenthesis right parenthesis squared end root
space space space space space equals space square root of 1 space plus space 7 squared end root space equals space square root of 1 space plus space 49 end root space equals space square root of 50 space equals space 5 square root of 2
DA space equals space square root of left parenthesis negative 3 plus 1 right parenthesis squared plus left parenthesis 5 plus 4 right parenthesis squared end root
space space space space space equals space square root of 4 space plus space 81 end root space equals space square root of 85
यहाँ   AB not equal to BC not equal to CD not equal to DA
अत: यह चतुर्भुज है जिसकी भुजाएँ बराबर नहीं हैं।