Q17. - Algebra 2

Question

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

Step-by-Step Solution

Answer

The coordinates of midpoint of the line segment are $\left(\frac{1}{24},\frac{1}{8}\right)$.

Step 1. Write down the given information.

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

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 $\left(\frac{1}{3},\frac{3}{4}\right)\text{ and }\left(-\frac{1}{4},-\frac{1}{2}\right)$.

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

Step 4. Conclusion.

The coordinates of midpoint of the line segment are $\left(\frac{1}{24},\frac{1}{8}\right)$.