Question

If P(9a-2, -b) divides the line segment joining A(3a+1, -3) and B(8a, 5) in the ratio 3:1. Find the values of a & b.

Answer 1

P(9a-2,b) = (x,y)
A(3a+1.-3) = (x1,y1)
B(8a,5) = (x2,y2)
Ratio (m1,m2) = 3,1

x = m1*x2 + m2*x1
      ---------------------
            m1 + m2
9a-2 =3*8a +1* 3a+1
           -----------------
                  3 + 1
9a-2 = 24a + 3a + 1
            ----------------
                    4
36a - 8 = 27a + 1
36a - 27a= 1 + 8 
9a = 9
a = 9
     -----
      9
a = 1

Now,


y = m1*y2 + m2*y1
      ---------------------
            m1 + m2
-b = 3*5 + 1 * -3
       ----------------
               4
-b = 15 - 3
        --------
            4
-b = 12/4
-b = 3
b = -3

Therefore a = 1, b = -3
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Answer 2

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