3(iii)
Use graph sheet for this question. Take 2 cm = 1 unit along the axes. Plot and write coordinates of:
(a) A (2, 3) and B (4, 5).
(b) image of A and B in the x-axis as A′ and B′.
(c) image of A′ in the y-axis as A″.
(d) name the single transformation that maps A to A″.
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(a) The points A (2, 3) and B (4, 5) are plotted on the graph :
(b) From figure,
On reflecting points A and B in the x-axis, we get :
A′ = (2, −3) and B′ = (4, −5).
(c) From figure,
On reflecting point A' in y-axis, we get :
A″ = (−2, −3).
(d) Point A (2, 3) is mapped to A″ (−2, −3).
Since both the coordinates change their signs, the single transformation that maps A to A″ is a reflection in the origin.
Hence, the single transformation that maps A to A″ is reflection in the origin.