The graph of $y = f(x)$ is symmetric across the line $x = 5$. The graph also passes through the point $(8,-7).$ Find another point that must lie on the graph of $y = f(x).$

Answer 1

Since the graph of $y = f(x)$ is symmetric across the line $x=5,$ it also passes through the point $(2,-7)$ with $x$-coordinate that is $2$ units away from the line of symmetry. Therefore, the point $(2,-7)$ must also lie on the graph of $y=f(x).$

Answer 2

what bot said, just noting that f(5-x) = f(5+x)
among all that word jumble