Ideas in Geometry/Instructive examples/Section 1.3

http://commons.wikimedia.org/wiki/File:Miset_1.3.jpg

In city geometry and regular geometry, a parabola is a set of points such that each of those points is the same distance from a given point, A, as it is from a given line, L.

1. 19 - Find the City Geometry midset of (-2,2) and (3,2).

To find the midset (a midset is a set of points that are equal distance between two points A and B) of two points in city geometry first find the distance between the two points. To find the distance between 2 points you subtract the 2 y's (y-y2) and add the difference of the x's (x-x2) so using this formula we can see d(a-b)= (-2 - 3) + (2-2) = 5 (find absolute value). Next find the halfway point between the distance of the points: 5/2 = 2.5 (Draw a city geometry circle with radius 2.5 to find where the two points will intersect. Once you find that intersection line you must check to see if more points will be an equal distance away from each point by moving up and down or right and left. Once you have checked all directions and have found the overlapping points you have found the midset you are looking for.