Question

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

Explanation:

Step1: Find the coordinates of the original points

From the graph, we can see that the coordinates of point \(C\) are \((-7,6)\), the coordinates of point \(D\) are \((2,6)\), and the coordinates of point \(E\) are \((-7,3)\).

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 \(C(-7,6)\), after reflection, the new point \(C'(-7,-6)\).
For point \(D(2,6)\), after reflection, the new point \(D'(2,-6)\).
For point \(E(-7,3)\), after reflection, the new point \(E'(-7,-3)\).

Step3: Plot the new points and connect them

Plot the points \(C'(-7,-6)\), \(D'(2,-6)\) and \(E'(-7,-3)\) on the coordinate plane and connect them to form the reflected triangle \(\triangle C'D'E'\).

Answer:

The coordinates of the reflected triangle \(\triangle C'D'E'\) are \(C'(-7,-6)\), \(D'(2,-6)\) and \(E'(-7,-3)\). Plot these points and connect them.