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निर्देशांक ज्यामिति

Question

Wired Faculty App

x तथा y में संबंध ज्ञात कीजिए यदि बिंदु (x, y), (1, 2) तथा (7, 0) संरेखी हैं।

Solution

तीन बिंदु यदि संरेखी हैं तो

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 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 close square brackets space equals space 0

therefore space space 1 half left square bracket straight x left parenthesis 2 minus 0 right parenthesis plus 1 left parenthesis 0 minus straight y right parenthesis plus 7 left parenthesis straight y minus 2 right parenthesis right square bracket equals 0 space space rightwards double arrow space 1 half left square bracket 2 straight x minus straight y plus 7 straight y minus 14 right square bracket equals 0 space rightwards double arrow space 1 half left square bracket 2 straight x plus 6 straight y minus 14 right square bracket equals 0 space rightwards double arrow space 2 straight x plus 6 straight y minus 14 equals 0 space rightwards double arrow space straight x plus 3 straight y minus 7 equals 0

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