Precalculus, Chapter 1, 1.2, Section 1.2, Problem 36

Plot the point $(4,0)$ 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

$(4,0) \to (4,0)$







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

$(4,0) \to (-4,0)$







c. The origin

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

$(4,0) \to (-4,0)$