point v lies on $overline{tu}$, where t is located at (-6, -4) and u is located at (10, 4). the ratio of tv to vu is 5:3. what are the coordinates of v? write your answers as integers or decimals.

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Accepted Answer

# Explanation:
## Step1: Recall the section - formula
If a point $V(x,y)$ divides the line - segment joining $T(x_1,y_1)$ and $U(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-6,y_1=-4,x_2 = 10,y_2 = 4,m = 5,n = 3$.
## Step2: Calculate the x - coordinate of $V$
$$
\begin{align*}
x&=\frac{5\times10+3\times(-6)}{5 + 3}\
&=\frac{50-18}{8}\
&=\frac{32}{8}\
& = 4
\end{align*}
$$
## Step3: Calculate the y - coordinate of $V$
$$
\begin{align*}
y&=\frac{5\times4+3\times(-4)}{5 + 3}\
&=\frac{20 - 12}{8}\
&=\frac{8}{8}\
&=1
\end{align*}
$$
# Answer:
$(4,1)$

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Question

Explanation:

Step1: Recall the section - formula

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

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

Answer: