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त्रिभुज

Question
CBSEHHIMAH10010494

सिध्द कीजिए की एक त्रिभुज, जिसके शीर्ष (t,t-2),(t+2,t+2) तथा (t+3,t) है, का क्षेत्रफल t से स्वतंत्र है।

Solution
म ा न ा space straight A left parenthesis straight t comma straight t minus 2 right parenthesis comma space straight B left parenthesis straight t plus 2 comma straight t plus 2 right parenthesis comma space straight C left parenthesis straight t plus 3 comma straight t right parenthesis
क ् ष े त ् रफल space increment ABC
equals space begin inline style 1 half end style space left square bracket straight x subscript 1 space left parenthesis straight y subscript 2 space minus space straight y subscript 3 right parenthesis space plus space straight x subscript 2 left parenthesis straight y subscript 3 space minus space straight y subscript 1 right parenthesis space plus space straight x subscript 3 left parenthesis straight y subscript 1 space minus space straight y subscript 2 right parenthesis right square bracket
equals space begin inline style 1 half end style space left square bracket straight t left parenthesis straight t space plus 2 space minus straight t right parenthesis space plus space left parenthesis straight t space plus space 2 right parenthesis left parenthesis straight t space minus space left parenthesis straight t space minus space 2 right parenthesis right parenthesis space plus space left parenthesis straight t space plus space 3 right parenthesis left parenthesis left parenthesis straight t space minus space 2 right parenthesis space minus space left parenthesis straight t space plus space 2 right parenthesis right parenthesis right square bracket
equals space begin inline style 1 half end style space left square bracket straight t left parenthesis 2 right parenthesis space plus space left parenthesis straight t space plus space 2 right parenthesis left parenthesis 2 right parenthesis space plus space left parenthesis straight t space plus space 3 right parenthesis left parenthesis negative 4 right parenthesis right square bracket
equals space begin inline style 1 half end style space left square bracket 2 straight t space plus space 2 straight t space plus space 4 space minus 4 straight t space minus 12 right square bracket
equals space begin inline style 1 half end style space left square bracket negative 8 right square bracket
equals space minus 4
space space space space space space increment space क ा space क ् ष े त ् रफल space हम े श ा space धन ा त ् मक left parenthesis plus ve right parenthesis space ह ो ग ा। space
space space space space space space increment space क ा space क ् ष े त ् रफल space equals space 4 space sq. space space य ू न ि ट comma space ज ो क ि space straight t space पर space न ि र ् भर space ह ैं।