6. given $overline{wy}$ with $w(3,7)$ and $y(13, - 8)$, if $x$ partitions $overline{wy}$ such that the ratio of $wx$ to $xy$ is $3:2$, find the coordinates of $x$.

Question

Accepted Answer

# Explanation:
## Step1: Recall section - formula
The section - formula for a point $P(x,y)$ that divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$ is given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, the ratio of $WX$ to $XY$ is $3:2$, so the point $X$ divides the line - segment $\overline{WY}$ in the ratio $3:2$, where $W(x_1,y_1)=(3,7)$ and $Y(x_2,y_2)=(13, - 8)$, and $m = 3$, $n = 2$.
## Step2: Calculate the x - coordinate of $X$
Using the formula $x=\frac{mx_2+nx_1}{m + n}$, we substitute $x_1 = 3$, $x_2=13$, $m = 3$, and $n = 2$.
$$
\begin{align*}
x&=\frac{3\times13+2\times3}{3 + 2}\
&=\frac{39 + 6}{5}\
&=\frac{45}{5}\
&=9
\end{align*}
$$
## Step3: Calculate the y - coordinate of $X$
Using the formula $y=\frac{my_2+ny_1}{m + n}$, we substitute $y_1 = 7$, $y_2=-8$, $m = 3$, and $n = 2$.
$$
\begin{align*}
y&=\frac{3\times(-8)+2\times7}{3 + 2}\
&=\frac{-24 + 14}{5}\
&=\frac{-10}{5}\
&=-2
\end{align*}
$$

# Answer:
The coordinates of $X$ are $(9,-2)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall section - formula

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

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

Answer: