Question

in the figure below, k lies between j and l. find the location of k so that the ratio of jk to kl is 4 to 1. j -22 k? l -2 location of k :

Explanation:

Step1: Identify the formula for the section - formula on a number line

If a point $K$ divides the line - segment joining $J(x_1)$ and $L(x_2)$ in the ratio $m:n$, then the coordinate of $K$ is given by $x=\frac{mx_2+nx_1}{m + n}$. Here, $x_1=-22$, $x_2=-2$, $m = 4$, and $n = 1$.

Step2: Substitute the values into the formula

$x=\frac{4\times(-2)+1\times(-22)}{4 + 1}$.
First, calculate the numerator: $4\times(-2)+1\times(-22)=-8-22=-30$.
Then, calculate the denominator: $4 + 1=5$.

Step3: Find the value of $x$

$x=\frac{-30}{5}=-6$.

Answer:

$-6$