point n lies on the segment mp. the coordinates of n so that the ratio of mn to np is 3 to 4. 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, $m = 3$, $n = 4$, $x_1=-4$, $y_1 = 6$, $x_2=17$, $y_2=-22$.
## Step2: Calculate the $x$ - coordinate of $N$
Substitute the values into the $x$ - coordinate formula:
$$
\begin{align*}
x&=\frac{3\times17+4\times(-4)}{3 + 4}\
&=\frac{51-16}{7}\
&=\frac{35}{7}\
& = 5
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of $N$
Substitute the values into the $y$ - coordinate formula:
$$
\begin{align*}
y&=\frac{3\times(-22)+4\times6}{3 + 4}\
&=\frac{-66 + 24}{7}\
&=\frac{-42}{7}\
&=-6
\end{align*}
$$

# Answer:
$(5,-6)$

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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: