10. given $overline{jl}$ with $j(8, - 8)$ and $l(-16, -2)$, find the coordinates of $k$ if $k$ divides $overline{jl}$ two - thirds of the way from $j$ to $l$.

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Accepted Answer

# Explanation:
## Step1: Recall section - formula
The formula to find the coordinates of a point $K(x,y)$ that divides the line - segment joining $J(x_1,y_1)$ and $L(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 2$, $n = 1$, $x_1=8$, $y_1=-8$, $x_2=-16$, $y_2=-2$.
## Step2: Calculate the x - coordinate of $K$
$$
\begin{align*}
x&=\frac{2\times(-16)+1\times8}{2 + 1}\
&=\frac{-32 + 8}{3}\
&=\frac{-24}{3}\
&=-8
\end{align*}
$$
## Step3: Calculate the y - coordinate of $K$
$$
\begin{align*}
y&=\frac{2\times(-2)+1\times(-8)}{2 + 1}\
&=\frac{-4-8}{3}\
&=\frac{-12}{3}\
&=-4
\end{align*}
$$
# Answer:
The coordinates of $K$ are $(-8,-4)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall section - formula

Step2: Calculate the x - coordinate of \(K\)

Step3: Calculate the y - coordinate of \(K\)

Answer: