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the line segment PQ joining the points P(2,-4) and Q(5,2) is trisected at the points R(3,a) and S(b,0). find the values of a and b.

Answer :

kvnmurty
We can solve this by finding the lengths of the segments PR and SQ and PQ. We can find the answers also by slopes.

P (2, -4)        R (3, a)        S (b,0)        Q (5, 2)
   PRSQ is a straight line.

 Slope of line PR = Slope of PQ
        (a+4) / (3-2) = (2+4) / (5-2) = 2
         a = -2

 Slope of line SQ  = Slop of PQ
        (2-0) / (5-b) = 2          =>  5-b = 1    => b = 4
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we can verify if needed the lengths of the line segments :
      PR = √(2²+1²) = √5            RS = √5    SQ = √5      PQ = √(6²+3²) = 3√5

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