Question

The point P (3, 4) is reflected to P’ in the x-axis; and O’ is the image of O (the origin) when reflected in the line PP’. Write: 

(i) the co-ordinates of P’ and O’. 

(ii) the length of the segments PP’ and OO’. 

(iii) the perimeter of the quadrilateral POP’O’.

(iv) the geometrical name of the figure POP’O’.

Answer 1

(i) Co-ordinates of P’ and O’ are (3, -4) and (6, 0) respectively. 

(ii) PP’ = 8 units and OO’ = 6 units. 

(iii) From the graph it is clear that all sides of the quadrilateral POP’O’ are equal. 

In right Δ PO’Q, PO’ = √(4)2 + (3)2 = 5 units So, perimeter of quadrilateral POP’O’ = 4 PO’ = 4 × 5 units = 20 units 

(iv) Quadrilateral POP’O’ is a rhombus.