given $overline{ac}$ with $a(3, 4)$ and $c(-9, -2)$, if $b$ partitions $ac$ such that the ratio of $ab$ to $bc$ is $1:5$, find the coordinates of $b$.

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Accepted Answer

# Explanation:
## Step1: Recall section - formula
The formula to find the coordinates of a point $B(x,y)$ that divides the line - segment joining $A(x_1,y_1)$ and $C(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1 = 3,y_1 = 4,x_2=-9,y_2=-2,m = 1,n = 5$.
## Step2: Calculate the x - coordinate of $B$
$$
\begin{align*}
x&=\frac{1\times(-9)+5\times3}{1 + 5}\
&=\frac{-9 + 15}{6}\
&=\frac{6}{6}\
&=1
\end{align*}
$$
## Step3: Calculate the y - coordinate of $B$
$$
\begin{align*}
y&=\frac{1\times(-2)+5\times4}{1 + 5}\
&=\frac{-2+20}{6}\
&=\frac{18}{6}\
&=3
\end{align*}
$$
# Answer:
The coordinates of $B$ are $(1,3)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall section - formula

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

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

Answer: