Answer:
(i) A"(-7, 6)
(ii) A"(3, 4)
Step-by-step explanation:
(i) The notation is a bit different. We assume it to mean that the transformation X is a translation 4 left and 2 up. That is, (-4, 2) gets added to the (x, y) coordinates:
(x, y) ⇒ (x -4, y +2)
For the coordinates A(1, 2), a transformation by X gives ...
A'(1 -4, 2+2) = A'(-3, 4)
We believe the notation X² is supposed to signify a second transformation by X. Then a second transformation by X of A' gives ...
A"(-3 -4, 4 +2) = A"(-7, 6) . . . A transformed by X²
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(ii) Reflection in the line x=0 negates the x-coordinate, so the transformation Y is ...
(x, y) ⇒ (-x, y)
Applying this transformation to the result of translating A by transformation X, we get ...
A" = (-(-3), 4) = A"(3, 4) . . . A transformed by XY
