A video game designer places an anthill at the origin of a coordinate plane. A red ant leaves the anthill and moves along a straight line to (1, 1), while a black ant leaves the anthill and moves along a straight
line to (-1, -1). Next, the red ant moves to (2, 2), while the
black ant moves to (-2, -2). Then the red ant
moves to (3, 3), while the black ant moves to (-3, -3), and so on. Complete the explanation of why the red
ant and the black ant are always the same distance from the anthill.
At any given moment, the red ant's coordinates may be written as (a, a) where > 0. The red ant's
distance from the anthill is
The black ant's coordinates may be written as (-a, a and the
black ant's distance from the anthill is
This shows that at any given moment, both ants are
units from the anthill.