Question

M is the midpoint of the line segment joining the point A (-3,7) and B(9,-1). Find the coordinates point M. Further R (2,2) divides the line segment joining M and B in the ration d: b. Find the ratio of d:b.

Answer 1

Mid point of AB

$M=\frac{-8+9}{2},\frac{7-1}{2}$

$M=\frac{6}{2}-\frac{6}{2}$

$M=(3,3)$

Now $R(2,2)$ divide M and B in ratio $d:b$

$2=\frac{9d+3b}{d+b}$, $2=\frac{-d+3b}{d+b}$

$2d+2b=9d+3b$, $2d+2b=-d+3b$

$-b=7d$ $3d=b$

By solving above equation we get different ratio in x and y

$\therefore$ We conclude that $R(2,2)$ does not divide $M(3,3)$

and $B(3,-1)$.