the point n lies on the segment mp. find the coordinates of n so that the ratio of mn to np is 3 to 5. coordinates of n :

Question

Accepted Answer

# Explanation:
## Step1: Use the section formula
The section formula for a point $N(x,y)$ that divides the line segment joining $M(x_1,y_1)$ and $P(x_2,y_2)$ in the ratio $m:n$ is given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 3$, $n=5$, $x_1=-6$, $y_1=-3$, $x_2 = 26$, $y_2=13$.
## Step2: Calculate the $x$ - coordinate of $N$
Substitute the values into the $x$ - coordinate formula:
$$
\begin{align*}
x&=\frac{3\times26+5\times(-6)}{3 + 5}\
&=\frac{78-30}{8}\
&=\frac{48}{8}\
&=6
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of $N$
Substitute the values into the $y$ - coordinate formula:
$$
\begin{align*}
y&=\frac{3\times13+5\times(-3)}{3 + 5}\
&=\frac{39-15}{8}\
&=\frac{24}{8}\
&=3
\end{align*}
$$

# Answer:
$(6,3)$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the section formula

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

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

Answer: