Mathematics
A point P is reflected in the x-axis. Co-ordinates of its image are (-4, 5).
(i) Find the co-ordinates of P.
(ii) Find the co-ordinates of the image of P under reflection in the y-axis.
Answer
(i) Reflection in x-axis is given by,
Mx(x, y) = (x, -y) ………(1)
Given, image of point P(x, y) on reflection in x-axis is (-4, 5)
Comparing with equation 1 we get,
(x, -y) = (-4, 5)
⇒ x = -4 and -y = 5
⇒ x = -4 and y = -5.
P = (x, y) = (-4, -5).
Hence, co-ordinates of P = (-4, -5).
(ii) Reflection in y-axis is given by,
My(x, y) = (-x, y)
Substituting (-4, -5) in above equation we get,
My(-4, -5) = (4, -5).
Hence, co-ordinates of image of P under reflection in y-axis = (4, -5).
Related Questions
State the co-ordinates of the following points under reflection in the line x = 0 :
(i) (-6, 4)
(ii) (0, 5)
(iii) (3, -4)
State the co-ordinates of the following points under reflection in the line y = 0 :
(i) (-3, 0)
(ii) (8, -5)
(iii) (-1, -3)
A point P is reflected in the origin. Co-ordinates of its image are (-2, 7).
(i) Find the co-ordinates of P.
(ii) Find the co-ordinates of the image of P under reflection in the x-axis.
The point P(a, b) is first reflected in the origin and then reflected in the y-axis to P'. If P' has co-ordinates (4, 6); evaluate a and b.