Chapter 4.7, Problem 30PPS

(a)

To determine

To graph: The congruent rectangles $ABCD$ and $WXYZ$ on a coordinate plane.

Explanation of Solution

Given information: The name of congruent rectangle should be $ABCD$ and $WXYZ$ .

Graph: The required rectangles are drawn below in a coordinate plane. Both rectangles $ABCD$ and $WXYZ$ are congruent.

(b)

To determine

To graph: The congruent rectangles $ABCD$ and $WXYZ$ on a coordinate plane.

Answer to Problem 30PPS

The rectangle $ABCD$ moves $5$ units to the right and then 4 units up.

Explanation of Solution

Given information: The following figure is taken from part (a)

We can see that in the figure, the rectangle $ABCD$ moves $5$ units to the right and then 4 units up, and formed $WXYZ$ which is congruent to $ABCD$ .

(c)

To determine

To fill: The given table.

Answer to Problem 30PPS

The table has been filled, given below.

  $\begin{array}{ccc}\begin{array}{l}\mathrm{Rectangle}\\ ABCD\end{array}& \text{Transformation}& \begin{array}{l}\text{Rectangle}\\ \text{WXYZ}\end{array}\\ A\left(0,0\right)& \left(0,5,0+4\right)& W\left(5,4\right)\\ B\left(0,2\right)& \left(0+5,2+4\right)& X\left(5,6\right)\\ C\left(3,2\right)& \left(3+5,2+4\right)& Y\left(8,6\right)\\ D\left(3,0\right)& \left(3+5,0+4\right)& Z\left(8,4\right)\end{array}$

Explanation of Solution

Given information: The following figure is taken from part (a)

Calculation: The coordinates of vertices the rectangles are filled in the table. Also the transformation is calculated, shown in figure.

  $\begin{array}{ccc}\begin{array}{l}\mathrm{Rectangle}\\ ABCD\end{array}& \text{Transformation}& \begin{array}{l}\text{Rectangle}\\ \text{WXYZ}\end{array}\\ A\left(0,0\right)& \left(0,5,0+4\right)& W\left(5,4\right)\\ B\left(0,2\right)& \left(0+5,2+4\right)& X\left(5,6\right)\\ C\left(3,2\right)& \left(3+5,2+4\right)& Y\left(8,6\right)\\ D\left(3,0\right)& \left(3+5,0+4\right)& Z\left(8,4\right)\end{array}$

(d)

To determine

To fill: The given blank spaces in rules of translation.

Answer to Problem 30PPS

The answer is $\left(x,y\right)\to \left(x+5,y+4\right)$ .

Explanation of Solution

Given information: $ABCD\to WXYZ:\left(x,y\right)\to \left(x+?,y+?\right)$

Calculation: Since $ABCD$ moves $5$ units to the right and then 4 units up, and formed $WXYZ$ which is congruent to $ABCD$ . Then the rule of translation is

  $ABCD\to WXYZ:\left(x,y\right)\to \left(x+5,y+4\right)$