Question

How do you find the midpoint of the line segment with endpoints $\left(\sqrt{50},1\right)$ and $\left(\sqrt{2},-1\right)$?

Answer 1

Use midpoint formula to compute coordinates of midpoint:

The midpoints of $\left(x_1,y_1\right),\left(x_2,y_2\right)$ is $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

Given points are $\left(\sqrt{50},1\right),\left(\sqrt{2},-1\right)$

Substituting the values in the midpoint formula:

$\begin{array}{rcl}\mathrm{Midpoint}& =& \left(\frac{\sqrt{50}+\sqrt{2}}{2},\frac{1-1}{2}\right)\\ & =& \left(\frac{5\sqrt{2}+\sqrt{2}}{2},0\right)\\ & =& \left(3\sqrt{2},0\right)\end{array}$

Hence, the midpoint of the line segment is at $\left(3\sqrt{2},0\right)$.