Rectangle WXYZ has a perimeter of 16 units and an area of 15 square units. Part A- Graph WXYZ on a sheet of graph paper. Write a composition of rigid motions describing two reflections of WXYZ across parallel lines of your choosing. Graph and label the parallel lines W'X'Y'Z' and W"X"Y"Z". Part B- Write a single rigid motion that is equivalent to the composition of rigid motions in Part A. Justify your answer. Part C- Compare the perimeter and area of WXYZ and W"X"Y"Z". What can you conclude about the effect of translation on the properties of figures?
Step 11 of 3
We solve for the dimensions, and , of the rectangle first. We are given that the perimeter is 16 units so we can write:
We are also given that the area is 15 square units so we can write:
Solve for using (1):
Substitute to (2) and solve for :
Solve for the corresponding widths:
Using appropriate measures, units and units.