Question

1. 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 $l$.

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 \((-8,-4)\)