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निर्देशांक ज्यामिति

Question
CBSEHHIMAH10010055

निम्नलिखित में से प्रत्येक में k का मान ज्ञात कीजिए ताकि तीनों बिंदु सरेखी हों:
(7, –2), (5, 1), (3, k)

Solution

तीन बिंदु यदि रेखीय हैं, तो
straight x subscript 1 left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis plus straight x subscript 2 left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis plus straight x subscript 3 left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis space equals space 0
या  increment का क्षेत्रफल
    equals 1 half open square brackets straight x subscript 1 left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis space plus space straight x subscript 2 left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis space plus space straight x subscript 3 left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis close square brackets space equals space 0
अब, increment ABC का क्षेत्रफल
          equals space 1 half open square brackets 7 left parenthesis 1 minus straight k right parenthesis plus 5 left parenthesis straight k minus left parenthesis negative 2 right parenthesis plus 3 left parenthesis negative 2 minus 1 right parenthesis close square brackets
equals space 1 half open square brackets 7 minus 7 straight k plus 5 straight k plus 10 minus 9 close square brackets
equals space 1 half left square bracket 8 minus 2 straight k right square bracket space equals space 4 minus straight k
           
          rightwards double arrow space 4 minus straight k space equals space 0
rightwards double arrow space space straight k space equals space 4