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'.

• A. 25 units
• B. 16 units
• C. 20 units
• D. 22 units

Answer 1

The correct option is C

20 units

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)

OM = 3 units

MP = 4 units

In right angled $\Delta OMP$

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

$=3^2+4^2$

$=25$

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

$\therefore$ perimeter of POP'O' = 5 $\times$ 4 = 20 units