what are the coordinates of the point on the directed line segment from (-7,2) to (-4,-10) that partitions the segment into a ratio of 5 to 1?

Question

Accepted Answer

# Explanation:
## Step1: Recall the section - formula
The formula to find the coordinates of a point $P(x,y)$ that divides the line - segment joining $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $(x_1,y_1)=(-7,2)$, $(x_2,y_2)=(-4,-10)$, $m = 5$, and $n = 1$.
## Step2: Calculate the $x$ - coordinate
$$
\begin{align*}
x&=\frac{5\times(-4)+1\times(-7)}{5 + 1}\
&=\frac{-20-7}{6}\
&=\frac{-27}{6}\
&=-\frac{9}{2}=-4.5
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate
$$
\begin{align*}
y&=\frac{5\times(-10)+1\times2}{5 + 1}\
&=\frac{-50 + 2}{6}\
&=\frac{-48}{6}\
&=-8
\end{align*}
$$
# Answer:
$(-4.5,-8)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the section - formula

Step2: Calculate the \(x\) - coordinate

Step3: Calculate the \(y\) - coordinate

Answer: