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Example - 1 : Find the co-ordinate of the image of the point (-3, 5) under (i) reflection in the x- axis (ii) reflection in the y- axis and (iii) reflection in the origin.

Solution :

1. Mx (x, y) = (x, - y)
   
2. My (x, y) = (-x, y)
   
3. Mo (x, y) = (-x -y)
   

Example - 2 : The image of a point P under reflection in the x- axis is (-3, 5). Write down the coordinates of P. Also find My and Mo of the point P and verify whether Mx My = My Mx = Mo.

Solution :

Let P is (x, y), then Mx (x, y) = (x,- y)

Here x = -3, -y = 5

Coordinate of P is (-3, -5)

Now, My (P) = My (x, y) = (-x, y) = (3, -5)

Mo = Mo (P) = Mo (-3, -5) = (3, 5)

Mx My = Mx My (-3, -5) = Mx (-3, 5)

= (3, 5) = Mo

My Mx = My Mx (-3, -5) = My (3, -5)

= (3, 5) = Mo.