Precalculus, Chapter 1, 1.2, Section 1.2, Problem 38

Plot the point $(-3,0)$ then plot the point that is symmetric to it with respect to (a) the $x$-axis; (b) the $y$-axis; (c) the origin

a. The $x$-axis

If the point $(-x,y)$ is reflected over the $x$-axis, then the image is the point $(-x,-y)$. So

$(-3,0) \to (-3,0)$







The point has no symmetry over the $x$-axis because $y$-coordinate is .

b. The $y$-axis

If the point $(-x,y)$ is reflected over the $y$-axis, then the image is the point $(x,y)$. So

$(-3,0) \to (3,0)$







c. The origin

If the point $(-x,y)$ is reflected over the origin then the image is the point $(x,-y)$. So

$(-3,0) \to (3,0)$