Chapter 1.2, Problem 30AYU

In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the $x\text{-axis}$; (b) the $y\text{-axis}$; (c) the origin.

$(4,0)$

To determine

To find: For the given point $\text{A}(4,0)$, the points symmetric with respect to $x\text{-axis}$, $y\text{-axis}$ and the origin.

Answer to Problem 30AYU

The point symmetric to the $x\text{-axis}$ is $(4,0)$

The point symmetric to the $y\text{-axis}$ is $(-4,0)$

The point symmetric to the origin is $(-4,0)$

Explanation of Solution

Given:

The point $\text{A}(4,0)$

Calculation:

If a graph is symmetric with respect to the $x\text{-axis}$ and the point $\text{A}(4,0)$ is on the graph then the point $(4,0)$ is also on the graph.

If a graph is symmetric with respect to the $y\text{-axis}$ and the point $\text{A}(4,0)$ is on the graph then the point $(-4,0)$ is also on the graph.

If a graph is symmetric with respect to the origin and the point $\text{A}(4,0)$ is on the graph then the point $(-4,0)$ is on the graph.