Draw the graphs of the lines $x=-2$, and $y=3$. Write the vertices of the figure formed by these lines, the x-axis and the y-axis. Also, find the area of the figure.

Given:

The given equations are:

 $x=-2$, and $y=3$. 

To do:

We have to find the vertices of the figure formed by these lines, the x-axis and the y-axis and the area of the figure formed.

Solution:

To represent the above equations graphically we need at least two solutions for each of the equations.

Every point on the line $x=-2$ will have $x$ coordinate as $-2$.

Therefore, 

$x$	$-2$	$-2$
$y$	$0$	$3$

Every point on the line $y=3$ will have $y$ coordinate as $3$.

Therefore, 

$x$	$-2$	$0$
$y$	$3$	$3$

The equation of x-axis is $y=0$.

The equation of y-axis is $x=0$.

The above situation can be plotted graphically as below:

 

The lines AB and BC represent the equations $x=-2$ and $y=3$ respectively.

As we can see, the points of intersection of the lines AB, BC, x-axis and y-axis taken in pairs are the vertices of the required figure.

Hence, the vertices of the required figure are $(-2,0), (-2,3), (0,3)$ and $(0,0)$. 

We know that,

Area of a rectangle$=lb$

Length of the rectangle$=$ Distance between the points C and D.

Length of the rectangle$=3$ units.

Breadth of the rectangle$=$Distance between the points A and D.

Breadth of the rectangle$=2$ units.

Area of the rectangle ABCD$=3\times2$ sq. units

$=6$ sq. units. 

The area of the figure so formed is 6 sq. units.