Final Answer:
When reflecting a point across a vertical line, specifically x = 3 in this case, the x-coordinate of the reflected point changes while the y-coordinate remains the same. Therefore the correct option is b) (5, 4)
Step-by-step explanation:
To find the coordinates of A' after reflecting across the line x = 3, we'll apply the formula for reflecting a point across a vertical line. The formula states that to reflect a point (x, y) across the line x = a, the x-coordinate becomes 2a - x while the y-coordinate remains unchanged.
Given the point A (1, 4) and the line x = 3, we'll reflect A across this line.
The x-coordinate of the line of reflection is 3.
Using the formula for reflection across a vertical line, the x-coordinate of A' will be 2 * 3 - 1 = 6 - 1 = 5.
And the y-coordinate remains unchanged, which is 4.
Therefore, the coordinates of A' after reflecting across the line x = 3 are (5, 4).
Therefore the correct option is b) (5, 4)