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Question

In the given figure P(5, -3) and Q(3, y) are the points of trisection of the line segment joining A(7, -2) and B(1, -5). Then y equals

(a) 2                  (b) 4                      (c) -4                             (d) 52


Solution

a s space i t space i s space t r i s e c t i o n A P equals P Q equals Q B square root of left parenthesis 7 minus 5 right parenthesis squared plus left parenthesis negative 2 minus negative 3 right parenthesis squared end root equals square root of left parenthesis 5 minus 3 right parenthesis squared plus left parenthesis negative 3 minus y right parenthesis squared end root equals square root of left parenthesis 3 minus 1 right parenthesis squared plus left parenthesis y minus negative 5 right parenthesis squared end root square root of 4 plus 25 end root equals square root of 4 plus left parenthesis 3 plus y right parenthesis squared end root equals square root of 4 plus left parenthesis y plus 5 right parenthesis squared end root square root of 29 equals square root of 4 plus left parenthesis 3 plus y right parenthesis squared end root space space space space space space space space space space space space space space space 29 equals 4 plus left parenthesis 3 plus y right parenthesis squared 25 equals left parenthesis 3 plus y right parenthesis squared 3 plus y equals 5 y equals 2

option a

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