Question 14 Marks

The points $P (1,-1 ), Q ( 4,-1)$ and $R ( 4, 3)$ are reflected in $y-$axis. If the images are denoted by $P' , Q'$ , and $R'$ , then 
$(i)$ Find the co$-$ordinates of $P'Q'R' , Q'$ and $R'$
$(ii)$ What kind of figure is formed by $RR' Q' Q? $
$(iii)$ Find the perimeter of the figure $P'Q'R'$

Answer

$(i)$ Find the co-ordinates of $P^{\prime} Q^{\prime} R^{\prime}, Q^{\prime}$ and $R^{\prime}$
The co-ordinates are: $P^{\prime} Q^{\prime} R^{\prime}=(-1,-1) ; Q^{\prime}=(-4,-1) ; R^{\prime}=(-4,3)$
$(ii)$ What kind of figure is formed by RR' $Q^{\prime} Q^{\text {? }}$
A rectangle is formed by $RR' Q' Q.$
$(iii)$ Find the perimeter of the figure $P^{\prime} Q^{\prime} R^{\prime}$

The figure is a right angled triangle with sides $4$ units, $3$ units and $5$ units.
Here, height $=4$ units, base $=3$ units and
$\text { Hypotenuse }=\left(\sqrt{4}^2+3^2\right)$
$=\sqrt{16+9}$
$=\sqrt{25}$
$=5 \text { units }$
Perimeter $=$ height + base + hypotenuse
$=4+3+5$
$=12 \text { units }$

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