Question

the point k lies on the segment jl. find the coordinates of k so that the ratio of jk to kl is 7 to 1. j (-30,22) k (?,?) l (2,-2) coordinates of k : (, )

Explanation:

Step1: Recall section - formula

If a point $K(x,y)$ divides the line - segment joining $J(x_1,y_1)$ and $L(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-30,y_1 = 22,x_2 = 2,y_2=-2,m = 7,n = 1$.

Step2: Calculate the x - coordinate of K

$x=\frac{7\times2+1\times(-30)}{7 + 1}=\frac{14-30}{8}=\frac{-16}{8}=-2$.

Step3: Calculate the y - coordinate of K

$y=\frac{7\times(-2)+1\times22}{7 + 1}=\frac{-14 + 22}{8}=\frac{8}{8}=1$.

Answer:

$(-2,1)$