Question

the coordinates of the endpoints of $overline{bc}$ are $b(3, 2)$ and $c(8, 17)$. point $d$ is on $overline{bc}$ and divides it such that $bd:cd$ is $3:2$. what are the coordinates of $d$? write your answers as integers or decimals.

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, $x_1 = 3,y_1 = 2,x_2 = 8,y_2 = 17,m = 3,n = 2$.

Step2: Calculate the x - coordinate of D

$x=\frac{3\times8+2\times3}{3 + 2}=\frac{24 + 6}{5}=\frac{30}{5}=6$.

Step3: Calculate the y - coordinate of D

$y=\frac{3\times17+2\times2}{3 + 2}=\frac{51+4}{5}=\frac{55}{5}=11$.

Answer:

$(6,11)$