Question

X is the midpoint of line segment WZ. Y is the midpoint of line segment XZ. W is located at (12, 8) and Z is at (0, -4). What are the coordinates of Y?

Answer 1

The diagram above shows Y is the midpoint of line XZ while X is the midpoint of line WZ,

Formula to find the midpoint of a line is given below as,

$\text{Midpoint of a line = (}\frac{x_1+x_2}{2}),(\frac{y_1+y_2}{2})$

Where the coordinates of points W and Z are,

$\begin{gathered} W(x_{1,}y_1)=(12,8) \\ Z(x_2,y_2)=(0,\text{ -4)} \end{gathered}$

Substituting (x, y) coordinates to find the midpoint, X of line WZ,

$\begin{gathered} X=(\frac{12+0}{2}),(\frac{8+(-4)}{2})=(\frac{12}{2},\frac{8-4}{2})=(6,\frac{4}{2})=(6,2) \\ \text{Hence, the coordinates of X are (6, 2)} \end{gathered}$

Recall, Y is the midpoint of XZ,

Where the coordinates of points X and Z are,

$\begin{gathered} X(x_1,y_1)=(6,2)_{} \\ Z(x_2,y_2)=(0,-4) \end{gathered}$

Substituting (x, y) coordinates to find the midpoint, Y of line XZ,

$\begin{gathered} Y=(\frac{6+0}{2}),(\frac{2+(-4)}{2})=(\frac{6}{2}),(\frac{2-4}{2})=(3,\frac{-2}{2})=(3,-1) \\ \text{Hence, the coordinates of Y are (3, -1)} \end{gathered}$

The coordinates of point Y are (3, -1).