find the coordinates of point b on $overline{ac}$ such that the ratio of $overline{ab}$ to $overline{bc}$ is 1:4. a(-11, -7) c(12, -5) show your work here

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Accepted Answer

# Explanation:
## Step1: Recall the section - formula
If a point $B(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $C(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 1$, $n = 4$, $x_1=-11$, $y_1=-7$, $x_2 = 12$, and $y_2=-5$.
## Step2: Calculate the $x$ - coordinate of point $B$
$$
\begin{align*}
x&=\frac{1\times12+4\times(-11)}{1 + 4}\
&=\frac{12-44}{5}\
&=\frac{-32}{5}=-6.4
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of point $B$
$$
\begin{align*}
y&=\frac{1\times(-5)+4\times(-7)}{1 + 4}\
&=\frac{-5-28}{5}\
&=\frac{-33}{5}=-6.6
\end{align*}
$$
# Answer:
$(-6.4,-6.6)$

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Question

Explanation:

Step1: Recall the section - formula

Step2: Calculate the \(x\) - coordinate of point \(B\)

Step3: Calculate the \(y\) - coordinate of point \(B\)

Answer: