Point P (3, – 5) is reflected to P’ in the x- axis. Also P on reflection in the y-axis is mapped as P”. (iii) Find the middle point of the line segment P’ P”. (iv) On which co-ordinate axis does the middle point of the line segment P P” lie ?

(iii) Co-ordinates of P’ = (3,5)

Co-ordinates of P’’ = (-3,-5)

Here x₁ = 3, y₁ = 5 , x₂ = -3, y₂ = -5

Let Q(x,y) be the midpoint of P’P’’

By midpoint formula,

x = (x₁+x₂)/2

y = (y₁+y₂)/2

x = (3+-3)/2 = 0/2 = 0

y = (5+-5)/2 = 0/2 = 0

Hence the co-ordinate of midpoint of P’P’’ is (0,0) .

(iv) Co-ordinates of P = (3,-5)

Co-ordinates of P’’ = (-3,-5)

Here x₁ = 3, y₁ = -5 , x₂ = -3, y₂ = -5

Let R(x,y) be the midpoint of PP’’

By midpoint formula,

x = (x₁+x₂)/2

y = (y₁+y₂)/2

x = (3+-3)/2 = 0/2 = 0

y = (-5+-5)/2 = -10/2 = -5

So the co-ordinate of midpoint of PP’’ is (0,-5) .

Here x co-ordinate is zero.

Hence the point lies on Y-axis.