Question

The points $(4,1),(4,-1),(-4,1)$ and $(-4,-1)$ are the vertices of a rectangle. If the rectangle is reflected in the line $x=5$, find the coordinates of the reflected rectangle. Also, find the area and perimeter of the reflected rectangle.

Answer 1

The coordinates $A(4,1),B(4,-1),D(-4,1)$ and $C(-4,-1)$ are plotted to form a rectangle.

The rectangle so formed and the reflected rectangle is shown in figure.

It is reflected through $x=5$ then the coordinates of the new rectangle become

$A^{\prime }(6,1)$,$B^{\prime }(6,-1)$,$C^{\prime }(14,-1)$ and $D^{\prime }(14,1)$

Perimeter of $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }=A^{\prime }{B}^{\prime }+B^{\prime }{C}^{\prime }+C^{\prime }{D}^{\prime }+D^{\prime }{A}^{\prime }$

$=2+8+2+8=20$units

Area$=l\times b=B^{\prime }{C}^{\prime }\times C^{\prime }{D}^{\prime }=8\times 2=16$sq.units.