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'?

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

make a sketch, perform the transformations

You will see the result easily to be (-9,4)

To find the coordinates of A' after reflecting point A (3, 4) over the line x = 2, we can use the formula for reflecting a point over a vertical line:

A' = (2 * line of reflection - x-coordinate of A, y-coordinate of A)

Using this formula, we get:

A' = (2 * 2 - 3, 4) = (4 - 3, 4) = (1, 4)

Now, to find the coordinates of A' after reflecting it over the line x = -4, we use the same formula:

A' = (2 * line of reflection - x-coordinate of A, y-coordinate of A')

Using this formula with A' = (1, 4) and the line of reflection x = -4, we get:

A' = (2 * -4 - 1, 4) = (-8 - 1, 4) = (-9, 4)

Therefore, the coordinates of A' are (-9, 4).

Therefore, the correct answer is option (C) (-9, 4).

To find the coordinates of A' after it is reflected over the line x = 2, we need to find the distance between the point A and the line x = 2, and then move A that same distance in the opposite direction.

The distance between a point (x, y) and the vertical line x = a is given by the formula: Distance = |x - a|

In this case, the distance between the x-coordinate of A (which is 3) and the line x = 2 is |3 - 2| = 1. So, we move 1 unit to the left from the line x = 2 to find the x-coordinate of A', which is 2 - 1 = 1.

Since A is reflected over the line x = 2, only its x-coordinate changes. Therefore, the coordinates of A' become (1, 4).

Now, we need to find the coordinates of A'' after it is reflected over the line x = -4. Again, we use the same method. The distance between the x-coordinate of A' (which is 1) and the line x = -4 is |1 - (-4)| = 5. So, we move 5 units to the right from the line x = -4 to find the x-coordinate of A'', which is -4 + 5 = 1.

Like before, only the x-coordinate changes when A' is reflected over the line x = -4. Therefore, the coordinates of A'' remain (1, 4).

Therefore, the correct answer is (1, 4).