Question

bc has endpoints b(-8, 0) and c(13, 14). point d divides bc into two parts with lengths in a ratio of 2:5.
what are the two possible locations of d?

Explanation:

Step1: Recall the section - formula

If a point $D(x,y)$ divides the line - segment joining $B(x_1,y_1)$ and $C(x_2,y_2)$ in the ratio $m:n$, then the coordinates of $D$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-8,y_1 = 0,x_2=13,y_2 = 14,m = 2,n = 5$.

Step2: Calculate the x - coordinate of D

$x=\frac{2\times13+5\times(-8)}{2 + 5}=\frac{26-40}{7}=\frac{-14}{7}=-2$.

Step3: Calculate the y - coordinate of D

$y=\frac{2\times14+5\times0}{2 + 5}=\frac{28+0}{7}=4$.

Answer:

$(-2,4)$