Question

graph the image of \\( \triangle t u v \\) after a reflection over the \\( x \\)-axis.

Explanation:

Step1: Find the coordinates of the original triangle

From the graph, we can see that the coordinates of \(T\) are \((-5,-6)\), the coordinates of \(U\) are \((5,-6)\), and the coordinates of \(V\) are \((-4,-8)\).

Step2: Apply the reflection rule over the \(x\) - axis

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,-y)\).
For point \(T(-5,-6)\), after reflection, the new coordinates \(T'(-5,6)\).
For point \(U(5,-6)\), after reflection, the new coordinates \(U'(5,6)\).
For point \(V(-4,-8)\), after reflection, the new coordinates \(V'(-4,8)\).

Step3: Plot the new points

Plot the points \(T'(-5,6)\), \(U'(5,6)\), and \(V'(-4,8)\) on the coordinate plane and connect them to form the reflected triangle.

Answer:

Plot the points \(T'(-5,6)\), \(U'(5,6)\), \(V'(-4,8)\) and connect them.