what are the coordinates of the point on the directed line segment from (6, - 10) to (9, 8) that partitions the segment into a ratio of 1 to 5?

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, $(x_1,y_1)=(6, - 10)$, $(x_2,y_2)=(9,8)$, $m = 1$, and $n = 5$.
## Step2: Calculate the $x$ - coordinate
$$
\begin{align*}
x&=\frac{1\times9+5\times6}{1 + 5}\
&=\frac{9 + 30}{6}\
&=\frac{39}{6}\
&=\frac{13}{2}=6.5
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate
$$
\begin{align*}
y&=\frac{1\times8+5\times(-10)}{1 + 5}\
&=\frac{8-50}{6}\
&=\frac{-42}{6}\
&=-7
\end{align*}
$$
# Answer:
$(6.5,-7)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the section - formula

Step2: Calculate the \(x\) - coordinate

Step3: Calculate the \(y\) - coordinate

Answer: