Question

If P(17/3, -b/3) divides the line segment joining A (2a+1,6) and B(a,4) in the ratio 1:2. Find the value of a and b

Answer 1

From the formula - The point which divides a line segment AB in the ratio m:n is given by [(mx₂+nx₁)/(m+n),(my₂+ny₁)/(m+n)] whre A=(x₁,y₁),B=(x₂,y₂)

(assuming internal division by piont P)

So, x-coordinate of P is given by [1*a + 2*(2a+1)]/3 = 17/3

i.e a + 4a + 2 = 17

i.e a=3

y-coordinate is given by -b/3 = (1*4+2*6)/3

implies b = -16