Midpoint Formula Math Example 1

Solution

1. 1
   The midpoint of a segment is the average of the two endpoints' coordinates: $M = \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}\right)$. Averaging 'splits the difference' equally.
2. 2
   Identify the endpoints: $(x_1, y_1) = (2, 8)$ and $(x_2, y_2) = (6, 4)$. Compute the averages separately for $x$ and $y$.
3. 3
   Substitute: $M = \left(\frac{2+6}{2},\, \frac{8+4}{2}\right) = \left(\frac{8}{2},\, \frac{12}{2}\right) = (4, 6)$. Verify: the point $(4,6)$ lies exactly halfway between $(2,8)$ and $(6,4)$ — the distance from $(2,8)$ to $(4,6)$ equals the distance from $(4,6)$ to $(6,4)$ (both equal $\sqrt{8}$).