Question

Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axis). P and Q have co-ordinates (0, 5) (- 2, 4).
(i) P is invariant when reflected in an axis. Name the axis.
(ii) Find the image of Q on reflection in the axis found in (i).
(iii) (0, k) on reflection in the origin is invariant. Write the value of k.
(iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin following by reflection in x-axis.

Answer 1

(i) The axis is y-axis or x = 0.
(ii) Image of 'Q'
Q' = M_{x = 0}(-2, 4)
= (2, 4)
(iii) ∵ M₀ (a, b) = (-a, -b)
∴ M₀ (0, k) = (o, -k)
∴  k = -k
∴  2k = 0
∴  k = 0
(iv) Q'' = MxMoQ
= M_xM₀ (-2, 4)
= Mx (2, -4)
= (-2, -4)