When we have two points on a number line, we can find the midpoint between them. Let's start with point A at negative 2 and point B at positive 4. The distance between these points is 6 units.
The midpoint formula states that the midpoint equals the sum of the two coordinates divided by 2. For our example with A at negative 2 and B at 4, the midpoint is negative 2 plus 4, divided by 2, which equals 1. This point M divides the line segment into two equal parts.
Now let's prove that the midpoint creates equal distances. The distance from A to M is the absolute value of 1 minus negative 2, which equals 3. The distance from M to B is the absolute value of 4 minus 1, which also equals 3. Since both segments have the same length, we've confirmed that M is indeed the midpoint.
Let's try another example with point C at negative 3 and point D at 5. Using our midpoint formula, we get negative 3 plus 5, divided by 2, which equals 1. To verify, the distance from C to M is 4 units, and the distance from M to D is also 4 units, confirming our calculation is correct.