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)
done
To find the coordinates of A' after reflecting A over the line x = 2, we can use the formula for reflecting a point over a vertical line.
The formula for reflecting a point (x, y) over the line x = h is:
(x', y) = (2h - x, y)
In this case, the line of reflection is x = 2, so h = 2. Now we can substitute the coordinates of point A (3, 4) into the formula:
(x', y) = (2(2) - 3, 4)
Simplifying:
(x', y) = (4 - 3, 4)
(x', y) = (1, 4)
After reflecting A over the line x = 2, the new coordinates of A' are (1, 4).
To find the coordinates of A' after reflecting A' over the line x = -4, we can use the same formula:
(x', y) = (2h - x, y)
In this case, the line of reflection is x = -4, so h = -4. Now we can substitute the coordinates of A' (1, 4) into the formula:
(x', y) = (2(-4) - 1, 4)
Simplifying:
(x', y) = (-8 - 1, 4)
(x', y) = (-9, 4)
After reflecting A' over the line x = -4, the new coordinates of A' are (-9, 4).
Therefore, the correct answer is:
(-9, 4)