# Ideas in Geometry/Instructive examples/Finding a Midset (21 from 1.3)

1.3 #21 Find the City Geometry midset of (-2,2) and (2,2).

To begin, first plot the two points on a grid.

A (-2,2) B(2,2)

Now that the points are plotted, you need to find the midset. A midset is a set of points that are equal distance away from two points. So, you need to find all the points that are the same distance from both A and B.

In the picture above all of the points labeled are equal distance away from A and B. 2 units to the right of A and 2 units to the left of B end up at the same point so this is part of the midset. To get to the points directly above and below this point, it is 3 units from both A and B. The picture also points that are 4, 5, and 6 units away from both A and B. All of these points are in the midset.

If you look closely at the points in the midset, all of the points are part of a line that bisects the line segment AB (divides it in two equal sections). They all have an x value of 0. Thus, any point that falls on this bisecting line is part of the midset. So, the midset of (-2,2) and (2,2) is a vertical line extending infinitely that bisects AB.

The blue line represents the midset.

Rachel89 21:23, 24 October 2010 (UTC)