To reflect a point across the y-axis, you change the sign of the x-coordinate while keeping the y-coordinate the same.
Given the points of triangle \( A'B'C' \):
- \( A'(1, 5) \) becomes \( A''(-1, 5) \)
- \( B'(7, 2) \) becomes \( B''(-7, 2) \)
- \( C'(9, 5) \) becomes \( C''(-9, 5) \)
Thus, the new coordinates for triangle \( A''B''C'' \) after reflecting across the y-axis are:
- \( A''(-1, 5) \)
- \( B''(-7, 2) \)
- \( C''(-9, 5) \)