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).