the coordinates of the endpoints of $overline{ef}$ are $e(-16, -12)$ and $f(-4, 0)$. point $g$ is on…

the coordinates of the endpoints of $overline{ef}$ are $e(-16, -12)$ and $f(-4, 0)$. point $g$ is on $overline{ef}$ and divides it such that $eg:fg$ is $3:1$. what are the coordinates of $g$? write your answers as integers or decimals.

the coordinates of the endpoints of $overline{ef}$ are $e(-16, -12)$ and $f(-4, 0)$. point $g$ is on $overline{ef}$ and divides it such that $eg:fg$ is $3:1$. what are the coordinates of $g$? write your answers as integers or decimals.

Answer

Explanation:

Step1: Recall the section - formula

If a point $G(x,y)$ divides the line - segment joining $E(x_1,y_1)$ and $F(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-16,y_1=-12,x_2=-4,y_2 = 0,m = 3,n = 1$.

Step2: Calculate the x - coordinate of G

$x=\frac{3\times(-4)+1\times(-16)}{3 + 1}=\frac{-12-16}{4}=\frac{-28}{4}=-7$.

Step3: Calculate the y - coordinate of G

$y=\frac{3\times0+1\times(-12)}{3 + 1}=\frac{0 - 12}{4}=-3$.

Answer:

$(-7,-3)$