what are the coordinates of the point on the directed line segment from (-5, -10) to (2, 4) that partitions the segment into a ratio of 2 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 $A(x_1,y_1)$ 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, $x_1=-5,y_1=-10,x_2 = 2,y_2 = 4,m = 2,n = 5$.
## Step2: Calculate the x - coordinate
$$
\begin{align*}
x&=\frac{2\times2+5\times(-5)}{2 + 5}\
&=\frac{4-25}{7}\
&=\frac{-21}{7}\
&=-3
\end{align*}
$$
## Step3: Calculate the y - coordinate
$$
\begin{align*}
y&=\frac{2\times4+5\times(-10)}{2 + 5}\
&=\frac{8-50}{7}\
&=\frac{-42}{7}\
&=-6
\end{align*}
$$
# Answer:
$(-3,-6)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the section - formula

Step2: Calculate the x - coordinate

Step3: Calculate the y - coordinate

Answer: