Question

1. given directed line segment (overline{km}), find the coordinates of (l) such that the ratio of (kl) to (km) is 1:3. plot point (l).

Explanation:

Step1: Recall the section - formula

If a point $L(x,y)$ divides the line - segment joining $K(x_1,y_1)$ and $M(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 1$ and $n=2$ (since the ratio of $KL$ to $KM$ is $1:3$, so $KL:LM=1:2$).

Step2: Assume coordinates of $K$ and $M$

Let's assume $K(x_1,y_1)$ and $M(x_2,y_2)$. From the graph, if we assume $K(- 4,-4)$ and $M(6,4)$.

Step3: Calculate the $x$ - coordinate of $L$

$x=\frac{1\times6+2\times(-4)}{1 + 2}=\frac{6-8}{3}=-\frac{2}{3}$.

Step4: Calculate the $y$ - coordinate of $L$

$y=\frac{1\times4+2\times(-4)}{1 + 2}=\frac{4 - 8}{3}=-\frac{4}{3}$.

Answer:

The coordinates of $L$ are $(-\frac{2}{3},-\frac{4}{3})$