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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:
(-1, -2), (1, 0), (-1, 2), (-3, 0)

Solution

माना A=(-1, -2), B=(1, 0), C=(-1, 2) तथा D=(-3, 0)

AB space equals space square root of left parenthesis negative 1 minus 1 right parenthesis squared plus left parenthesis negative 2 minus 0 right parenthesis squared end root space space space space space equals space square root of left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared end root space equals space square root of 4 space plus space 4 end root space equals space 2 square root of 2 BC space equals space square root of left parenthesis 1 plus 1 right parenthesis squared plus left parenthesis 0 minus 2 right parenthesis squared end root space space space space space equals space square root of 2 squared space plus space 2 squared end root space equals space square root of 4 space plus space 4 end root space equals space 2 square root of 2 CD space equals space square root of left parenthesis negative 1 plus 3 right parenthesis squared plus left parenthesis 2 minus 0 right parenthesis squared end root space space space space space equals space square root of 2 squared space plus space 2 squared end root space equals space square root of 4 space plus space 4 end root space equals space 2 square root of 2 DA space equals space square root of left parenthesis negative 1 plus 3 right parenthesis squared plus left parenthesis negative 2 minus 0 right parenthesis squared end root space space space space space equals space square root of 2 squared space plus space left parenthesis negative 2 right parenthesis squared end root space equals space square root of 4 space plus space 4 end root space equals space 2 square root of 2 AC space equals space square root of left parenthesis negative 1 plus 1 right parenthesis squared plus left parenthesis 2 plus 2 right parenthesis squared end root space space space space space equals space square root of 0 space plus space 16 end root space equals space square root of 16 space equals space 4 BD space equals space square root of left parenthesis negative 3 minus 1 right parenthesis squared plus left parenthesis 0 plus 0 right parenthesis squared end root space space space space space equals space square root of 16 space plus space 0 end root space equals space square root of 16 space equals space 4

यहाँ AB = BC = CD = DA तथा AC = BD
अत: चतुर्भुज वर्ग होगा।

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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