Question

The point $(2,3)$ is reflected four times about co-ordinate axes continuously starting with $x$-axis. The area of the quadrilateral formed in sq. units is

• A. $24$
• B. $6$
• C. $12$
• D. $5$

Answer 1

The correct option is A $24$

Let the vertex $A=(2,3)$

Taking the image about x axis, we get $B=(2,-3)$

Again taking the image about y axis we get $C=(-2,-3)$

Taking the image about x axis, we get $D=(-2,3)$

Again taking the image above axis gives us $A=(2,3)$

Hence the vertices of the quadrilateral so formed are

$A=(2,3)$
$B=(2,-3)$
$C=(-2,-3)$
$D=(-2,3)$

It is a rectangle as all the interior angles are ${90}^0$ since the transformations are above the co-ordinate axes.

Application of distance formula, gives us

$AB=CD=6units$
$BC=AD=4units$

Hence area will be product of adjacent sides.

$AB=6units$
$BC=4units$

Hence

$Area=6\times 4$
$=24$ sq units.