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Communicate Mathematical Ideas A video game designer places an anthill at the origin of a...

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Communicate Mathematical Ideas 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. Explain why the red ant and the black ant are always the same distance from the anthill.

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