Question

point x on the coordinate plane for each situ 2. point x on $overline{rs}$ is $\frac{1}{6}$ of the distance from $r$ to $s$. $r(-4,2)$ $s(2,-2)$

Explanation:

Step1: Recall the section - formula

If a point $X(x,y)$ divides the line - segment joining $R(x_1,y_1)$ and $S(x_2,y_2)$ 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 $n=5$ (since $X$ is $\frac{1}{6}$ of the distance from $R$ to $S$, the ratio of $RX$ to $XS$ is $1:5$), $x_1=-4$, $y_1 = 2$, $x_2=2$, and $y_2=-2$.

Step2: Calculate the $x$ - coordinate of $X$

$x=\frac{1\times2+5\times(-4)}{1 + 5}=\frac{2-20}{6}=\frac{-18}{6}=-3$.

Step3: Calculate the $y$ - coordinate of $X$

$y=\frac{1\times(-2)+5\times2}{1 + 5}=\frac{-2 + 10}{6}=\frac{8}{6}=\frac{4}{3}$.

Answer:

$X(-3,\frac{4}{3})$