Question

Find the midpoint of line segment with endpoints at given coordinates \[\left( \frac{1}{2},-\frac{2}{3} \right)\text{ and }\left( \frac{1}{3},\frac{1}{4} \right)\].

Short answer

The coordinates of midpoint of the line segment are \[\left( \frac{5}{12},-\frac{5}{24} \right)\].

Step-by-step solution

Step 1. Write down the given information.

The given line segment with end-points has coordinates $\left(\frac{1}{2},-\frac{2}{3}\right)\text{and}\left(\frac{1}{3},\frac{1}{4}\right)$.

Step 2. Concept used.

If a line segment has end-points at $\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$then the midpoint of the segment has coordinates $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

Step 3. Calculation.

The coordinates of the midpoint are evaluated using the points$\left(\frac{1}{2},-\frac{2}{3}\right)\text{and}\left(\frac{1}{3},\frac{1}{4}\right)$.

$\begin{array}{c}\text{Midpoint}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)A\\ =\left(\frac{\frac{1}{2}+\frac{1}{3}}{2},\frac{-\frac{2}{3}+\frac{1}{4}}{2}\right)\\ =\left(\frac{1}{4}+\frac{1}{6},-\frac{2}{6}+\frac{1}{8}\right)\\ =\left(\frac{5}{12},-\frac{5}{24}\right)\end{array}$

Step 4. Conclusion.

The coordinates of midpoint of the line segment are$\left(\frac{5}{12},-\frac{5}{24}\right)$.