Question

If point $(\frac{1}{2},y)$ lies on the line segment joining the points A (3 , -5) and B (-7, 9), then find the ratio in which P divides AB. also find the value of y .

Answer 1

$P(\frac{1}{2},y)$ lies on AB,line AB \implies $y+5=\frac{14}{-10}(x-3)$

P lies on the line =>$y=\frac{-3}{2}$

=>P$(\frac{1}{2},\frac{-3}{2})$,$A(3,-5)$ & $B(-7,9)$

Let the ratio it cuts Ab be m:n=>$(\frac{1}{2},\frac{-3}{2})$$=(\frac{-7m+3n}{m+n},\frac{9m-5n}{m+n})$

=>$m:n=1:3$