find the coordinates of the point that partitions $overline{ab}$ in the ratio 3:7.
the point that partitions $overline{ab}$ in the ratio 3:7 is
(simplify your answer. type an ordered pair.)

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, $A(-4,-7)$, $B(12,5)$, $m = 3$, and $n = 7$.
## Step2: Calculate the x - coordinate
$$
\begin{align*}
x&=\frac{3\times12+7\times(-4)}{3 + 7}\
&=\frac{36-28}{10}\
&=\frac{8}{10}\
&=\frac{4}{5}=0.8
\end{align*}
$$
## Step3: Calculate the y - coordinate
$$
\begin{align*}
y&=\frac{3\times5+7\times(-7)}{3 + 7}\
&=\frac{15-49}{10}\
&=\frac{-34}{10}\
&=-\frac{17}{5}=-3.4
\end{align*}
$$
# Answer:
$(0.8,-3.4)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the section - formula

Step2: Calculate the x - coordinate

Step3: Calculate the y - coordinate

Answer: