QQuestion
Use a graph sheet for this question.
(a) Plot A(0, 3), B(2, 1) and C(4, −1).
(b) Reflect points B and C in the y-axis and name their images B′ and C′ respectively. Plot and write the coordinates of B′ and C′.
(c) Reflect point A in the line BB′ and name its image A′.
(d) Plot and write the coordinates of A′.
(e) Join the points ABA′B′ and give the geometrical name of the closed figure so formed.
✓Answer
(a) Plot A(0, 3), B(2, 1) and C(4, −1) on the graph.
(b) Reflection in the y-axis changes (x, y) to (−x, y).
Therefore:
B(2, 1) → B′(−2, 1)
C(4, −1) → C′(−4, −1)
(c) The line BB′ passes through B(2, 1) and B′(−2, 1), so its equation is y = 1.
Reflecting A(0, 3) in y = 1 places its image the same perpendicular distance below the line.
Distance of A from y = 1 is 3 − 1 = 2 units.
Therefore, A′ is 2 units below y = 1.
A′ = (0, −1)
(d) The required coordinates are:
A′(0, −1), B′(−2, 1) and C′(−4, −1).
(e) On joining A, B, A′ and B′, all four sides are equal and adjacent sides are perpendicular.
Therefore, ABA′B′ is a square.
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