Question

Find the midpoint of line segment with endpoints at given coordinates $\left(5,9\right)\text{and}\left(12,18\right)$.

Short answer

The coordinates of midpoint of the line segment are $\left(8.5,13.5\right)$.

Step-by-step solution

Step 1. Write down the given information.

The given line segment with end-points has coordinates $\left(5,9\right)\text{and}\left(12,18\right)$.

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 $\left(5,9\right)\text{and}\left(12,18\right)$.

$\begin{array}{c}\text{Midpoint}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{5+12}{2},\frac{9+18}{2}\right)\\ =\left(\frac{17}{2},\frac{27}{2}\right)\\ =\left(8.5,13.5\right)\end{array}$

Step 4. Conclusion.

The coordinates of midpoint of the line segment are $\left(8.5,13.5\right)$.