Given the point $A(5,2)$, what are the coordinates of $A\text{'}$ after reflecting across the line $x=3$?

• A. $(2,5)$
• B. $(1,2)$
• C. $(3,2)$
• D. $(5,4)$

Answer: (B)

Verified step by step guidance

1. Identify the original point A with coordinates \( (5, 2) \) and the line of reflection \( x = 3 \).
2. Understand that reflecting a point across a vertical line \( x = k \) changes the \( x \)-coordinate but keeps the \( y \)-coordinate the same.
3. Calculate the horizontal distance from the point to the line: \( d = 5 - 3 = 2 \).
4. Find the reflected point's \( x \)-coordinate by subtracting this distance from the line: \( x' = 3 - d = 3 - 2 \).
5. Keep the \( y \)-coordinate unchanged: \( y' = 2 \). Thus, the reflected point \( A' \) has coordinates \( (x', y') \).