Chapter F - Foundations: A Prelude to Functions - Section F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - F.2 Assess Your Understanding - Page 17: 34

(a) The symmetric point with respect to the x-axis for $(4,0)$ is $(4,0)$. (b) The symmetric point with respect to the y-axis for $(4,0)$ is $(-4,0)$. (c) The symmetric point with respect to the origin for $(4,0)$ is $(-4,0)$. Refer to the plot below.

The point that is symmetric to the given point with respect to the $x$-axis can be reached by changing the coordinate from $(x,y)$ to $(x,-y)$: The symmetric point with respect to the $x$-axis for $(4,0)$ is $(4,0)$. The point that is symmetric to the given point with respect to the $y$-axis can be reached by changing the coordinate from $(x,y)$ to $(-x,y)$: The symmetric point with respect to the $y$-axis for $(4,0)$ is $(-4,0)$. The point that is symmetric to the given point with respect to the origin can be reached by changing the coordinate from $(x,y)$ to $(-x,-y)$: The symmetric point with respect to the origin for $(4,0)$ is $(-4,0)$.