The midpoint of a segment with endpoints (x1,y1) and (x2,y2) is:

The midpoint of a segment with endpoints (x1,y1) and (x2,y2) is:

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

Answer: (A)

The midpoint is the point exactly halfway along the segment, so each coordinate is the average of the corresponding endpoints. For the x-coordinates, halfway between x1 and x2 is (x1 + x2)/2, and for the y-coordinates, halfway between y1 and y2 is (y1 + y2)/2. A quick way to see this is to parameterize points on the segment as (x, y) = (x1, y1) + t((x2 − x1), (y2 − y1)); the midpoint occurs at t = 1/2, which gives ((x1 + x2)/2, (y1 + y2)/2). This is why the given expression is the correct midpoint. The other forms mix differences or omit the division by 2 on one coordinate, so they do not place the point at the center between the endpoints.

The midpoint is the point exactly halfway along the segment, so each coordinate is the average of the corresponding endpoints. For the x-coordinates, halfway between x1 and x2 is (x1 + x2)/2, and for the y-coordinates, halfway between y1 and y2 is (y1 + y2)/2. A quick way to see this is to parameterize points on the segment as (x, y) = (x1, y1) + t((x2 − x1), (y2 − y1)); the midpoint occurs at t = 1/2, which gives ((x1 + x2)/2, (y1 + y2)/2). This is why the given expression is the correct midpoint. The other forms mix differences or omit the division by 2 on one coordinate, so they do not place the point at the center between the endpoints.