Answer
(a) The symmetric point with respect to the $x$-axis for $(3,4)$ is $(3,-4)$.
(b) The symmetric point with respect to the $y$-axis for $(3,4)$ is $(-3,4)$.
(c) The symmetric point with respect to the origin for $(3,4)$ is $(-3,-4)$.
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 $(3,4)$ is $(3,-4)$.
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 $(3,4)$ is $(-3,4)$.
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 $(3,4)$ is $(-3,-4)$.
