Question

the point n lies on the segment mp. find the coordinates of n so that the ratio of mn to np is 4 to 5. m(-8,5) n(?,?) p(21,-13) coordinates of n: (?,?)

Explanation:

Step1: Recall section - formula

If a point $N(x,y)$ divides the line - segment joining $M(x_1,y_1)$ and $P(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-8,y_1 = 5,x_2=21,y_2=-13,m = 4,n = 5$.

Step2: Calculate the x - coordinate of N

$x=\frac{4\times21+5\times(-8)}{4 + 5}=\frac{84-40}{9}=\frac{44}{9}$.

Step3: Calculate the y - coordinate of N

$y=\frac{4\times(-13)+5\times5}{4 + 5}=\frac{-52 + 25}{9}=\frac{-27}{9}=-3$.

Answer:

$(\frac{44}{9},-3)$