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.
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Let us mark the points that is traced by the red ant and the black ant. Find the figure attached.
The red ant moves one unit each time from the origin on the quadrant 1 and the black ant moves one unit each time from the origin on the quadrant 3.
Combining the movement of both the ants we can see that they are moving form the origin along the line y=x and at every point they are at equal distance from the origin
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