Chapter 9, Problem 30RP

a

To determine

To find:The coordinate of point E.

Answer to Problem 30RP

The coordinates of point E : (9, − 3)

Explanation of Solution

Given information:

RECT is rectangle

  $\begin{array}{l}\overline{CE}\parallel y-\text{axis}\\ \overline{RE}\parallel x-\text{axis}\end{array}$

Formula used:

Reflection rule

Calculation :

Since, point E is the reflation of point R through negative y axis

  $\therefore$ x - coordinate of point E will same as of point R but with positive sign and

also, point E is reflection of point C through positive x − axis

  $\therefore$ y - coordinate of point E will same as of point C but with negative sign

Thus, Coordinates of point E is (9, − 3)

b

To determine

To find: The area of the rectangle.

Answer to Problem 30RP

The area of RECT is $140{\text{ units}}^2$

Explanation of Solution

Given information:

RECT is rectangle

  $\begin{array}{l}\overline{CE}\parallel y-\text{axis}\\ \overline{RE}\parallel x-\text{axis}\end{array}$

Formula used:

Area of rectangle = length $\times$ breadth

Calculation :

RE = $\sqrt{{\left(-9-5\right)}^2+{\left(-3+3\right)}^2}=14\text{ units}$

CE = $\sqrt{{\left(9-9\right)}^2+{\left(7+3\right)}^2}=10\text{ units}$

Now,

Area of RECT =

  $\begin{array}{l}RE\times CE\\ \text{=14}\times {\text{10=140 unit}}^2\end{array}$

c

To determine

To calculate:The length of diagonal of rectangle.

Answer to Problem 30RP

The length of rectangle is $2\sqrt{74}\text{ units}$

Explanation of Solution

Given information:

RECT is rectangle

  $\begin{array}{l}\overline{CE}\parallel y-\text{axis}\\ \overline{RE}\parallel x-\text{axis}\end{array}$

Formula used:

Distance formula

Calculation :

Distance between R and C is RC

RC =

  $\begin{array}{l}\sqrt{{\left(-5-9\right)}^2+{\left(-3-7\right)}^2}\\ =\sqrt{196+100}\\ =\sqrt{296}\\ =2\sqrt{74}\text{ units}\\ \text{=8}\text{.6 units}\end{array}$