Question

The point A (3, 4) is reflected over the line x = 2, and then is reflected over the line x = -4. What are the coordinates of A'?

(9, 4)
(-9, 4)
(1, 4)
(1, 2)

Answer 1

I think it’s (-9, 4)

Answer 2

9514 1404 393

Answer:

(-9, 4)

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).

_____

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.