One number is less than a second number. five times the first is 1 more than 3 times the second. find the numbers

Let the numbers be represented by "a" and "b".
 a < b
 5a = 1 +3b
Then
 a = (1 +3b)/5
So we can substitute for "a" to gete
 (1 +3b)/5 < b
 1 +3b < 5b
 1 < 2b
 1/2 < b

The conditions will be met for any numbers "a" and "b" such that
 b > 1/2
 a = (1 +3b)/5

Integer solutions will be solutions to the Diophantine equation
 5a -3b = 1
which has solutions (for n ≥ 1)
 a = 3n -1
 b = 5n -2
The smallest pair of integers meeting the requirement is 2 and 3.

Dcups i think

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.