Question

the coordinates of the endpoints of $overline{tu}$ are $t(-2,7)$ and $u(4, - 8)$. point $v$ is on $overline{tu}$ and divides it such that $tv:uv$ is $1:2$. what are the coordinates of $v$? write your answers as integers or decimals.

Explanation:

Step1: Recall the section - formula

If a point $V(x,y)$ divides the line - segment joining $T(x_1,y_1)$ and $U(x_2,y_2)$ in the ratio $m:n$, then the coordinates of $V$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-2,y_1 = 7,x_2 = 4,y_2=-8,m = 1,n = 2$.

Step2: Calculate the x - coordinate of V

$x=\frac{1\times4+2\times(-2)}{1 + 2}=\frac{4-4}{3}=0$.

Step3: Calculate the y - coordinate of V

$y=\frac{1\times(-8)+2\times7}{1 + 2}=\frac{-8 + 14}{3}=\frac{6}{3}=2$.

Answer:

$(0,2)$