An arithmetic sequence has a a geometric sequence has a common

An arithmetic sequence has a common DIFFERENCE.

This means that the difference between a term and the previous one is always the same. For example: 1, 4, 7, 10, 13,... This is an arithmetic sequence because the difference between consecutive elements is always 3 (4-1=7-4=10-7=13-10=...=3)

A geometric sequence has a common RATIO.

This means that the ratio between a term and the previous one is always the same. For example: 1, 3, 9, 27, 81,... This is a geometric sequence because the ratio between consecutive elements is always 3
(3/1=9/3=27/9=81/27=...=3).

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.