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A point (2, n) is 5 units away from the point $$(-1,3)$$. What is the product of all possible integer values for n?

Mar 20, 2022

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The two points are 3 units across from each other.

For the 2 points to be exactly 5 units apart from each other, we need a 3 - 4 - 5 right triangle, because one of the legs is a 3, and the hypotenuse is a 5.

The only points that meet these conditions are $$(2,7)$$ and $$(2, -1)$$.

Thus, $$n$$ can equal $$-1$$ or $$7$$, and the answer is $$-1 \times 7 =$$___.

Mar 20, 2022