Question

the point k lies on the segment jl. find the coordinates of k so that jk is ⅕ of jl. j(-2, -5) l(3, 5) 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 $m:n$, the coordinates of $K$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 1$ and $n=4$ (since $JK=\frac{1}{5}JL$, so the ratio of $JK$ to $KL$ is $1:4$), $J(-7,-15)$ and $L(3,5)$.

Step2: Calculate the x - coordinate of $K$

$x=\frac{1\times3 + 4\times(-7)}{1 + 4}=\frac{3-28}{5}=\frac{-25}{5}=-5$.

Step3: Calculate the y - coordinate of $K$

$y=\frac{1\times5+4\times(-15)}{1 + 4}=\frac{5-60}{5}=\frac{-55}{5}=-11$.

Answer:

$(-5,-11)$