Question

ed onto the second shape by doing two different
what those two transformations are.
#6
the shape was
and then

Explanation:

Step1: Analyze the translation

Looking at the \(x -\)coordinates of corresponding points (e.g., point \(W\) has an \(x -\)coordinate of \(2\) and \(W''\) has an \(x -\)coordinate of \(- 3\)). The change in the \(x -\)coordinate is \(\Delta x=-3 - 2=-5\). So, there is a translation (slide) \(5\) units to the left.

Step2: Analyze the rotation

After the translation, observe the orientation of the shape. The original shape (with points \(W,X,Y,Z\)) and the translated - rotated shape (with points \(W'',X'',Y'',Z''\)). By comparing the angles between the sides of the two shapes (using the grid to check the slopes of the sides), we can see that the shape is rotated \(90^{\circ}\) counter - clockwise (or \(270^{\circ}\) clockwise). We can also use the property of rotation: if we consider a point \((x,y)\) rotated \(90^{\circ}\) counter - clockwise about the origin becomes \((-y,x)\) (after translation, we can assume a local origin for the shape analysis).

Answer:

The shape was translated \(5\) units to the left and then rotated \(90^{\circ}\) counter - clockwise (or \(270^{\circ}\) clockwise).