The point P divide the join of (2, 1) and (-3, 6) in the ratio 2 : 3. Does P lie on the line x - 5y + 15 = 0 ?

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Solution

$g i v e n space t h e space p o i n t space P space d i v i d e s space t h e space j o i n t space o f space open parentheses 2 comma 1 close parentheses space a n d space open parentheses negative 3 comma 6 close parentheses space i n space t h e space r a t i o space 2 colon 3 c o minus o r d i n a t e s space o f space p o i n t space P space a r e open parentheses fraction numerator 2 cross times negative 3 plus 3 cross times 2 over denominator 2 plus 3 end fraction comma fraction numerator 2 cross times 6 plus 3 cross times 1 over denominator 2 plus 3 end fraction close parentheses equals open parentheses 0 comma 3 close parentheses s u b s t i t u t i n g space x equals 0 space a n d space y equals 3 space i n space t h e space g i v e n space e q u a t i o n comma w e space h a v e L. H. S equals 0 minus 5 open parentheses 3 close parentheses plus 15 equals 0 equals R. H. S h e n c e space t h e space p o i n t space P space l i e s space o n space t h e space l i n e space x minus 5 y plus 15 equals 0$

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