Question

Using graph paper, (take $2cm=1$ unit on both axis), plot $A(-4,2)$ and $B(2,4)$. $A^{\prime }$ is the image of $A$ when reflected in the $y$-axis. Plot it on the graph paper and write the coordinates of $A^{\prime }$. $B^{\prime }$ is the image of $B$ when reflected about the line $A{A}^{\prime }$. Join $A-B-A^{\prime }-B^{\prime }$ and name the quadrilateral.

Answer 1

$A^{\prime }$ is the image of $A$ about the $y$-axis. Hence, if $A\equiv (x,y)$ then $A^{\prime }=(-x,y)$.

$\therefore A^{\prime }=(4,2)$

$A{A}^{\prime }$ is a horizontal line. Hence, the $x$-coordinate of the reflection of $B$ about $A{A}^{\prime }$ will be the same. Also, $B$ is vertically $2$ units above line $A{A}^{\prime }$. So $B^{\prime }$ should be $2$ units vertically below $A{A}^{\prime }$.

$\therefore B^{\prime }=(2,0)$

The obtained figure is a Kite.