What is the midpoint formula for two points (x1, y1) and (x2, y2)?

• A. ((x1 + x2)/2, (y1 + y2)/2)
• B. ((x1 - x2)/2, (y1 - y2)/2)
• C. ((x1 + y2)/2, (y1 + x2)/2)
• D. ((x1 x2)/2, (y1 y2)/2)

Answer: (A)

The midpoint is the point exactly halfway between two points, so you treat each coordinate separately. The x-coordinate of the midpoint is halfway between x1 and x2, which is (x1 + x2)/2. The y-coordinate is halfway between y1 and y2, which is (y1 + y2)/2. Put together, the midpoint is ((x1 + x2)/2, (y1 + y2)/2). This makes sense because you’re averaging the two x-values to land midway on the horizontal axis and averaging the two y-values to land midway on the vertical axis. For example, between (0,0) and (2,6) the midpoint is ((0+2)/2, (0+6)/2) = (1,3). The other forms either halve a difference, mix coordinates incorrectly, or multiply coordinates, none of which give the point halfway along the segment.