Question

The point P(3, 4) is reflected to P' in the x axis and O' is the image of O(0, 0) when reflected in the line PP'. Find the perimeter of the quadrilateral POP'O'.$\left[4Marks\right]$

Answer 1

$\left[1Mark\right]$

P (3, 4) when reflected in X axis is P'(3, -4)

Equation of line PP' is x = 3

$\therefore$ image of O(0, 0) in the line PP' is O'(6, 0)
$\left[1Mark\right]$

OM = 3 units

MP = 4 units
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In right angled $\Delta OMP$

$O{P}^2=O{M}^2+M{P}^2$

$=3^2+4^2$

$=25$

$\Rightarrow OP=\sqrt{25}=5$

Similarly, the other sides of the quadrilateral are also of 5 units.

$\therefore$ Perimeter of POP'O' = 5 $\times$ 4 = 20 units
$\left[1Mark\right]$