Question

the coordinates of the endpoints of $overline{rs}$ are $r(2,7)$ and $s(14, - 5)$. point $t$ is on $overline{rs}$ and divides it such that $rt:st$ is $5:1$. what are the coordinates of $t$? write your answers as integers or decimals.

Explanation:

Step1: Recall the section - formula

If a point $T(x,y)$ divides the line - segment joining $R(x_1,y_1)$ and $S(x_2,y_2)$ in the ratio $m:n$, then the coordinates of $T$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1 = 2,y_1 = 7,x_2 = 14,y_2=-5,m = 5,n = 1$.

Step2: Calculate the x - coordinate of $T$

$x=\frac{5\times14+1\times2}{5 + 1}=\frac{70 + 2}{6}=\frac{72}{6}=12$.

Step3: Calculate the y - coordinate of $T$

$y=\frac{5\times(-5)+1\times7}{5 + 1}=\frac{-25 + 7}{6}=\frac{-18}{6}=-3$.

Answer:

$(12,-3)$