#### Question

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?

#### Solution

Verified#### Step 1

1 of 3We solve for the dimensions, $l$ and $w$, of the rectangle first. We are given that the perimeter is 16 units so we can write:

$2l+2w=16$

$\color{#4257b2}{l+w=8}\tag{1}$

We are also given that the area is 15 square units so we can write:

$\color{#4257b2}{ lw=15}\tag{2}$

Solve for $w$ using (1):

$w=8-l$

Substitute to (2) and solve for $l$:

$l(8-l)=15$

$8l-l^2=15$

$0= l^2-8l+15$

$0=(l-5)(l-3)$

$l=3,5$

Solve for the corresponding widths:

$w=8-3=5\text{ and }w=8-5=3$

Using appropriate measures, $l=5$ units and $w=3$ units.