Question

what two rigid transformations were performed on figure abcd to produce the congruent figure wxyz?

Explanation:

Step1: Analyze horizontal movement

The \(x\) - coordinates of the vertices of figure \(ABCD\) are \(x_A=-6,x_B = - 6,x_C=-4,x_D=-3\). The \(x\) - coordinates of the vertices of figure \(WXYZ\) are \(x_W = 2,x_X=0,x_Y=-1,x_Z = 3\). The change in \(x\) - coordinate for each point is \(x\) - value of new point minus \(x\) - value of old point. For example, for point \(A\) and \(X\), \(0-(-6)=6\). So, there is a translation of 6 units to the right.

Step2: Analyze vertical movement

The \(y\) - coordinates of the vertices of figure \(ABCD\) are \(y_A=-3,y_B=-5,y_C=-6,y_D=-2\). The \(y\) - coordinates of the vertices of figure \(WXYZ\) are \(y_W = 9,y_X=9,y_Y=7,y_Z = 6\). The change in \(y\) - coordinate for each point is \(y\) - value of new point minus \(y\) - value of old point. For example, for point \(A\) and \(X\), \(9-(-3)=12\). So, there is a translation of 12 units up.

Answer:

A translation 6 units to the right and 12 units up.