Answer
(a) The symmetric point with respect to the $x$-axis for $(5,3)$ is $(5,-3)$.
(b) The symmetric point with respect to the y-axis for $(5,3)$ is $(-5,3)$.
(c) The symmetric point with respect to the origin for $(5,3)$ is $(-5,-3)$.
Refer to the plot below.
Work Step by Step
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 $(5,3)$ is $(5,-3)$.
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 $(5,3)$ is $(-5,3)$.
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 $(5,3)$ is $(-5,-3)$.
