Chapter 10.2, Problem 4AYU

The point that is symmetric with respect to the $x\text{-axis}$ to the point is_______. (pp.19-21)

To determine

To find: The point symmetric with respect to $x\text{-axis}$ to the point $\left(-2,5\right)$.

Answer to Problem 4AYU

$\left(-2,-5\right)$

Explanation of Solution

Given:

The points $\left(-2,5\right)$.

Formula used:

A graph is said be symmetric with respect to $x\text{-axis}$ if, for every point $\left(x,y\right)$ on the graph, the point $\left(x,\mathrm{-y}\right)$ is also on the graph.

Calculation:

Consider the points $\left(-2,5\right)$ on the graph.

In general the point symmetric with respect to $x\text{-axis}$ to the point $\text{(}x,y\text{)}$ is $\text{(}x,\mathrm{-y}\text{)}$.

The point symmetric to $\left(-2,5\right)$ is $\left(-2,\mathrm{-5}\right)$.