Chapter 12.5, Problem 11E

To determine

To find : reflection in the $x-axis$

Explanation of Solution

Given information : The question is to find the reflection in the $x-axis$ of the vertices $A\left(1,-2\right)B\left(3,-1\right)C\left(4,-4\right)$

Graph : The provided vertices is $A\left(1,-2\right)B\left(3,-1\right)C\left(4,-4\right)$

So, the $x$ - coordinates remain same and $y-$ coordinate will be multiplies by $-1$

  $\begin{array}{l}{A}^{\prime }=\left(1,-1\times -2\right)=\left(1,2\right)\\ B^{\prime }=\left(3,-1\times -1\right)=\left(3,1\right)\\ C^{\prime }=\left(4,-1\times -4\right)=\left(4,4\right)\end{array}$

Interpretation : The object is reflected in the $x-axis$ .