Question
Download Solution PDFABC एक समबाहु त्रिभुज है और AD, BC पर शीर्षलंब है। यदि A के निर्देशांक (1,2) हैं और D के निर्देशांक (−2,6) हैं, तो BC का समीकरण क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFगणना:
दिए गए शीर्ष A(1, 2) और D(−2, 6), जहाँ AD एक समबाहु त्रिभुज ABC में A से BC पर शीर्षलंब है।
AD की ढलान की गणना करें:
\(m_{AD} = \frac{\,y_D - y_A\,}{\,x_D - x_A\,} = \frac{\,6 - 2\,}{\,-2 - 1\,} = \frac{4}{-3} = -\tfrac{4}{3}.\)
क्योंकि AD ⟂ BC, BC की ढाल, \(m_{BC}\), संतुष्ट करती है
\(m_{AD} \cdot m_{BC} = -1 \;\Longrightarrow\; \Bigl(-\tfrac{4}{3}\Bigr) \,m_{BC} = -1 \;\Longrightarrow\; m_{BC} = \frac{-1}{\, -\tfrac{4}{3}\,} = \tfrac{3}{4}.\)
रेखा BC का समीकरण
\(y - 6 = \tfrac{3}{4}\,(x + 2).\)
\(4(y - 6) = 3(x + 2)\;\Longrightarrow\;4y - 24 = 3x + 6.\)
\(4y - 24 - 3x - 6 = 0 \)
\(\;\Longrightarrow\; -3x + 4y - 30 = 0 \;\Longrightarrow\; 3x - 4y + 30 = 0.\)
इसलिए, सही उत्तर विकल्प 4 है।
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