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CBSE Class 10 Answered

Find the values of k for which the points A(k+1,2k) , B(3k,2k+3) , C(5k-1,5k) are collinear.
Asked by amoghknightoo7 | 11 Mar, 2016, 11:12: AM
answered-by-expert Expert Answer
begin mathsize 16px style G i v e n space p o i n t s space w i l l space b e space c o l l i n e a r comma space i f space a r e a space o f space t h e space t r i a n g l e space f o r m e d space b y space t h e m space i s space z e r o. A r e a equals 1 half left square bracket x subscript 1 left parenthesis y subscript 2 minus y subscript 3 right parenthesis plus x subscript 2 left parenthesis y subscript 3 minus y subscript 1 right parenthesis plus x subscript 3 left parenthesis y subscript 1 minus y subscript 2 right parenthesis right square bracket rightwards double arrow 0 equals 1 half left square bracket left parenthesis k plus 1 right parenthesis left parenthesis 2 k plus 3 minus 5 k right parenthesis plus 3 k left parenthesis 5 k minus 2 k right parenthesis plus left parenthesis 5 k minus 1 right parenthesis left parenthesis 2 k minus 2 k minus 3 right parenthesis right square bracket rightwards double arrow 0 equals left parenthesis k plus 1 right parenthesis left parenthesis 3 minus 3 k right parenthesis plus 3 k left parenthesis 3 k right parenthesis plus left parenthesis 5 k minus 1 right parenthesis left parenthesis negative 3 right parenthesis rightwards double arrow 0 equals 3 k minus 3 k squared plus 3 minus 3 k plus 9 k squared minus 15 k plus 3 rightwards double arrow 0 equals 6 k squared minus 15 k plus 6 rightwards double arrow 0 equals 2 k squared minus 5 k plus 2 rightwards double arrow 0 equals 2 k squared minus 4 k minus k plus 2 rightwards double arrow 0 equals 2 k left parenthesis k minus 2 right parenthesis minus 1 left parenthesis k minus 2 right parenthesis rightwards double arrow 0 equals left parenthesis 2 k minus 1 right parenthesis left parenthesis k minus 2 right parenthesis rightwards double arrow 2 k minus 1 equals 0 space O R space k minus 2 equals 0 rightwards double arrow k equals 1 half space O R space k equals 2 end style
Answered by Rashmi Khot | 11 Mar, 2016, 12:55: PM

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