what are the coordinates of the point on the directed line segment from (-6,4) to (8,-10) that partitions the segment into a ratio of 1 to 6?

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Accepted Answer

# Explanation:
## Step1: Recall the section - formula
The formula for finding the coordinates of 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 $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-6,y_1 = 4,x_2 = 8,y_2=-10,m = 1,n = 6$.
## Step2: Calculate the x - coordinate
$$
\begin{align*}
x&=\frac{1\times8+6\times(-6)}{1 + 6}\
&=\frac{8-36}{7}\
&=\frac{-28}{7}\
&=-4
\end{align*}
$$
## Step3: Calculate the y - coordinate
$$
\begin{align*}
y&=\frac{1\times(-10)+6\times4}{1 + 6}\
&=\frac{-10 + 24}{7}\
&=\frac{14}{7}\
&=2
\end{align*}
$$
# Answer:
$(-4,2)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the section - formula

Step2: Calculate the x - coordinate

Step3: Calculate the y - coordinate

Answer: