Question

the point n lies on the segment $overline{mp}$. find the coordinates of n so that mn is $\frac{5}{7}$ of mp. p (28, 12) n (?,?) m (-7, -2) coordinates of n : ( , )

Explanation:

Step1: Use section - formula for x - coordinate

Let $M(x_1,y_1)=(-7,-2)$ and $P(x_2,y_2)=(28,12)$. The formula for the x - coordinate of a point $N$ that divides the line segment $MP$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$. Here, $m = 5$ and $n=7 - 5=2$.
$x=\frac{5\times28+2\times(-7)}{5 + 2}=\frac{140-14}{7}=\frac{126}{7}=18$

Step2: Use section - formula for y - coordinate

The formula for the y - coordinate of a point $N$ that divides the line segment $MP$ in the ratio $m:n$ is $y=\frac{my_2+ny_1}{m + n}$.
$y=\frac{5\times12+2\times(-2)}{5 + 2}=\frac{60 - 4}{7}=\frac{56}{7}=8$

Answer:

$(18,8)$