Question

A classmate tells you, “Finding the coordinates of a midpoint is easy. You just find the averages.” Is there any truth to it? Explain what you think your classmate means.

Answer 1

Your classmate is correct, though this is not explicitly what the midpoint formula is necessarily set out to do. If one is given two sets of endpoints, one can discover the midpoint by finding the mean distance between these two endpoints. For example, if two points are 10 and 2, all you need do to find the midpoint is add the two poles and divide them by 2 (that is, find the average). The same applies for coordinate geometry, except with additional variables, the formula to find the coordinates of a midpoint is: M= (x1+x2/2, y1+y2/2). Thus, two averages (of both the x coordinates and y coordinates are taken). Your classmate is correct if two endpoints are given, think of a line with two poles, the middle of this line must be the midpoint.