select the coordinates of point x on rs that is ⅙ of the distance from r to s. a) (3, -1⅓) b) (-3, 1⅓) c) (-3, -1⅓) d) (3, 1⅓) r(-4, 2) s(2, -2)

Question

Accepted Answer

# 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 $n=5$, $x_1=-4,y_1 = 2,x_2 = 2,y_2=-2$.
## Step2: Calculate the $x$ - coordinate of point $X$
$$
\begin{align*}
x&=\frac{1\times2+5\times(-4)}{1 + 5}\
&=\frac{2-20}{6}\
&=\frac{-18}{6}\
&=-3
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of point $X$
$$
\begin{align*}
y&=\frac{1\times(-2)+5\times2}{1 + 5}\
&=\frac{-2 + 10}{6}\
&=\frac{8}{6}\
&=1\frac{1}{3}
\end{align*}
$$

# Answer:
B. $(-3,1\frac{1}{3})$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the section - formula

Step2: Calculate the \(x\) - coordinate of point \(X\)

Step3: Calculate the \(y\) - coordinate of point \(X\)

Answer: