Question

the point k lies on the segment $overline{jl}$. find the coordinates of k so that the ratio of jk to kl is 1 to 3. l (4,2) k (?,?) j (-28, -22) coordinates of k : (, )

Explanation:

Step1: Recall the 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, $x_1=-28,y_1=-22,x_2 = 4,y_2 = 2,m = 1,n = 3$.

Step2: Calculate the x - coordinate of K

$x=\frac{1\times4+3\times(-28)}{1 + 3}=\frac{4-84}{4}=\frac{-80}{4}=-20$.

Step3: Calculate the y - coordinate of K

$y=\frac{1\times2+3\times(-22)}{1 + 3}=\frac{2-66}{4}=\frac{-64}{4}=-16$.

Answer:

$(-20,-16)$