Mathematics
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.
Answer
(i) Reflection in origin is given by,
Mo(x, y) = (-x, -y) ………(1)
Given, image of point P(x, y) on reflection in origin is (-2, 7)
Comparing with equation 1 we get,
(-x, -y) = (-2, 7)
⇒ -x = -2 and -y = 7
⇒ x = 2 and y = -7.
P = (x, y) = (2, -7).
Hence, co-ordinates of P = (2, -7).
(ii) Reflection in x-axis is given by,
Mx(x, y) = (x, -y)
Substituting (2, -7) in above equation we get,
Mx(2, -7) = (2, 7).
Hence, co-ordinates of image of P under reflection in x-axis = (2, 7).
Related Questions
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 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.
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.
The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A".
(i) Write down the co-ordinates of A".
(ii) Write down a single transformation that maps A onto A".