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The graph of $y = f(x)$ has the line $x = 5$ as an axis of symmetry. The graph also passes through the point $(8,-7).$ Find another point that must lie on the graph of $y = f(x).$

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 May 4, 2020
 #1
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the graph of \(y = f(x)\) has the line \(x=5\) as an axis of symmetry. the graph also passes through the point \((8, -7)\). find anohter point that must lie on the graph of \(y = f(x)\).
 

since \(x=5\) is the line of symmetry, we know that the point \((8, -7)\) reflected over \(x=5\) must also be on the graph of \(y = f(x)\)\((8, -7)\) is 3 units away from \(x=5\) on the \(y\)-axis, so the point 

\((8 - 2(8-5), -7) = (8 - 6, -7) = \boxed{(2, -7)}\)

must also be on the graph ​of \(y = f(x)\).

 May 4, 2020
 #2
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Nice solution!

LuckyDucky  May 4, 2020

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