the coordinates of the endpoints of $overline{lm}$ are $l(-7, -7)$ and $m(5, 9)$. point $n$ is on…

the coordinates of the endpoints of $overline{lm}$ are $l(-7, -7)$ and $m(5, 9)$. point $n$ is on $overline{lm}$ and divides it such that $ln:mn$ is $1:3$. what are the coordinates of $n$? write your answers as integers or decimals.

the coordinates of the endpoints of $overline{lm}$ are $l(-7, -7)$ and $m(5, 9)$. point $n$ is on $overline{lm}$ and divides it such that $ln:mn$ is $1:3$. what are the coordinates of $n$? write your answers as integers or decimals.

Answer

Explanation:

Step1: Recall the section - formula

If a point $N(x,y)$ divides the line - segment joining $L(x_1,y_1)$ and $M(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-7,y_1=-7,x_2 = 5,y_2 = 9,m = 1,n = 3$.

Step2: Calculate the x - coordinate of N

$x=\frac{1\times5+3\times(-7)}{1 + 3}=\frac{5-21}{4}=\frac{-16}{4}=-4$.

Step3: Calculate the y - coordinate of N

$y=\frac{1\times9+3\times(-7)}{1 + 3}=\frac{9-21}{4}=\frac{-12}{4}=-3$.

Answer:

$(-4,-3)$