day 1 - directed line segment
point a (2, 4) and b (12, 14). find the coordinates of p that divides $overline{ab}$ in a ratio of 1:4.

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, $x_1 = 2,y_1 = 4,x_2 = 12,y_2 = 14,m = 1,n = 4$.
## Step2: Calculate the $x$ - coordinate of $P$
$$
\begin{align*}
x&=\frac{1\times12 + 4\times2}{1+4}\
&=\frac{12 + 8}{5}\
&=\frac{20}{5}\
&=4
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of $P$
$$
\begin{align*}
y&=\frac{1\times14+4\times4}{1 + 4}\
&=\frac{14 + 16}{5}\
&=\frac{30}{5}\
&=6
\end{align*}
$$
# Answer:
The coordinates of $P$ are $(4,6)$

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Question

Explanation:

Step1: Recall the section - formula

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

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

Answer: