9514 1404 393
Answer:
(-9, 4)
Step-by-step explanation:
Reflection over the line x=a performs the transformation ...
(x, y) ⇒ (2a -x, y)
So, reflection over the two lines will give the transformation ...
(x, y) ⇒ (2·2 -x, y) = (4 -x, y) . . . . . reflection over x=2
then ...
(4 -x, y) ⇒ (2(-4)-(4-x), y) = (x -12, y) . . . followed by reflection over x=-4
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Reflecting (3, 4) over the two lines gives an image point of ...
(x, y) ⇒ (x -12, y)
(3, 4) ⇒ (3 -12, 4) = (-9, 4)
The coordinates of A' are (-9, 4).
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Comment on double reflection
Reflection over the two lines results in a translation that is double the distance between the two lines. The translation is in the direction that the second line is from the first. Here, the lines are 2 -(-4) = 6 units apart, with the second line being to the left of the first. The translation is 12 units to the left.
