Question

the coordinates of the endpoints of $overline{de}$ are $d(-8,7)$ and $e(4,3)$. point $f$ is on $overline{de}$ and divides it such that $ef:fd$ is $1:3$. what are the coordinates of $f$? write your answers as integers or decimals.

Explanation:

Step1: Recall the section - formula

If a point $F(x,y)$ divides the line - segment joining $D(x_1,y_1)$ and $E(x_2,y_2)$ in the ratio $m:n$, the coordinates of $F$ are given by $x=\frac{mx_1+nx_2}{m + n}$ and $y=\frac{my_1+ny_2}{m + n}$. Here, $x_1=-8,y_1 = 7,x_2 = 4,y_2 = 3,m = 3,n = 1$.

Step2: Calculate the x - coordinate of F

$x=\frac{3\times4+1\times(-8)}{3 + 1}=\frac{12-8}{4}=\frac{4}{4}=1$.

Step3: Calculate the y - coordinate of F

$y=\frac{3\times3+1\times7}{3 + 1}=\frac{9 + 7}{4}=\frac{16}{4}=4$.

Answer:

$(1,4)$