Midpoint of a line segment

Let S be a point with coordinates $(x_1, y_1)$, T with coordinates $(x_2, y_2)$, and M with coordinates $(x, y)$, where M is the midpoint of ST. Consider the figure below:

Considering the angles of the triangles SMC and TMD, the triangles SMC and TMD are similar since they are equiangular.

The coordinates of the midpoint $M$ of a line segment joining two points $S(x_1, y_1)$ and $T(x_2, y_2)$ are given by the following formula:

$$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$

Problem: Find the coordinates of the midpoint of the line segment joining the points $(-2, 8)$ and $(-4, -2)$.

Solution:

Let the coordinates of the points be: $S(x_1, y_1) = (-2, 8)$, $T(x_2, y_2) = (-4, -2)$

Using the midpoint formula:

$$M = \left( \frac{-2 + (-4)}{2}, \frac{8 + (-2)}{2} \right)$$ $$M = \left( \frac{-6}{2}, \frac{6}{2} \right)$$ $$M = (-3, 3)$$

Therefore, the coordinates of the midpoint of the line joining the points $(-2, 8)$ and $(-4, -2)$ are $(-3, 3)$.