Question

8. Plot P(0, 2) and Q(3, 2). Reflect P in the x-axis
to get P' and reflect Q in the origin to get Q'.
(i) Write the co-ordinates of P' and Q'.
(ii) What is the geometrical figure formed
by joining PQP'Q’?
(iii) Find its perimeter and area.
(iv) Name two points from the figure which
are invariant on reflection in y-axis.​

Answer 1

Answer:

Given,

P’ is the image of P (3, 4) reflected in x- axis and O’ is the image of O the origin in the line P’P.

(i) Hence, co-ordinates of P’ are (3, -4) and co-ordinates of O’ reflected in PP’ are (6, 0)

(ii) Length of PP’ = 8 units and OO’ = 6 units

(iii) Perimeter of POP’O’ is (4 x OP) units.

Let Q be the point of intersection of diagonals OO’ and PP’.

So, OQ = 3 units and OP = 4 units

Hence,

OP=√[(OQ)

2

+(PQ)

2

]=√(3

2

+4

2

)=√(9+16)=√25=5units

Thus, the perimeter of POP’O’ = 4 x 5 = 20 units