The following table shows the coordinates of points S, M and T. In each case, state whether M is the midpoint of segment ST. Justify your answer.

S	M	T	M mid of ST?	Reason
(-3, 0)	(0, 0)	(3, 0)
(2, 3)	(3, 4)	(4, 5)
(0, 0)	(0, 5)	(0, -10)
(-8, 7)	(0, -2)	(6, -3)

When M is the mid-point of ST, can you find any connection between the coordinates of M, S and T?

Since $M$ is the midpoint of $ST$ iff 

$M = \left( \frac{S_x + T_x}{2}, \frac{S_y + T_y}{2} \right)$.

Connection (the midpoint formula): If $m$ is the midpoint of segment ST, then

$$M_x = \frac{(S_x + T_x)}{2} \text{ and } M_y = \frac{(S_y + T_y)}{2}.$$

Equivalently, the coordinates of the midpoint are the averages of the coordinates of the two endpoints.