Question
Download Solution PDFयदि (4, x), (y, -5) और (7, 8) से बने किसी त्रिभुज का केन्द्रक (3, 5) है तो क्रमशः x और y के मान क्या हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
एक त्रिभुज का केंद्रक: वह बिंदु जहाँ त्रिभुज के तीन माध्यक प्रतिच्छेद करते हैं।
एक त्रिभुज पर विचार करें। यदि त्रिभुज के तीन शीर्ष A(x1, y1), B(x2, y2), C(x3, y3) हैं
त्रिभुज का केन्द्रक
=\(\rm (\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})\)
गणना:
यहाँ, त्रिभुज के शीर्ष (4,x), (y,-5) और (7, 8) और केन्द्रक = (3, 5)
इसलिए, 3 = \(\rm \frac{4+y+7}{3}\)
⇒11+y = 9
⇒ y = -2
और, 5 = \(\rm \frac{x-5+8}{3}\)
⇒ x + 3 = 15
⇒ x = 12
∴ x = 12, और y = -2
इसलिए, विकल्प (3) सही है।
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