Question

find the coordinates of point k on $overline{jl}$ such that the ratio of $jk$ to $jl$ is 1:2. j(7,3) l(1,2) show your work here

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 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, $J(7,3)$, $L(1,2)$, $m = 1$, and $n = 1$.

Step2: Calculate the x - coordinate of point K

$x=\frac{1\times1+1\times7}{1 + 1}=\frac{1 + 7}{2}=\frac{8}{2}=4$.

Step3: Calculate the y - coordinate of point K

$y=\frac{1\times2+1\times3}{1 + 1}=\frac{2+3}{2}=\frac{5}{2}=2.5$.

Answer:

The coordinates of point $K$ are $(4,2.5)$