Question

One last question, Line segment XZ has endpoints X(-2, 4) and Z(-8, -6). If Y is the midpoint of XZ, find the length of XY. Round to the nearest tenth. Anyone mind helping?

Answer 1

• Midpoint Formula: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$
• Distance Formula: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Firstly, we need to find where midpoint Y is. Plug in points X and Z into the midpoint formula to solve as such:

$Y=(\frac{-2+(-8)}{2},\frac{4+(-6)}{2})\\\\Y=(\frac{-10}{2},\frac{-2}{2})\\\\Y=(-5,-1)$

Now that we have the coordinates of Y, plug in points X and Y into the distance formula to find out their lengths as such:

$XY=\sqrt{(-2-(-5))^2+(4-(-1))^2}\\XY=\sqrt{3^2+5^2}\\XY=\sqrt{9+25}\\XY=\sqrt{34}\approx 5.8$

XY is approximately 5.8 units.