A point has the coordinates \( (0, k) \). Which reflection of the point will produce an image at the same coordinates, \( (0, k) \) ? a reflection of the point across the \( x \)-axis a reflection of the point across the \( y \)-axis a reflection of the point across the line \( y=x \) a reflection of the point across the line \( y=-x \)

If you reflect the point \( (0, k) \) across the \( x \)-axis, the image will be \( (0, -k) \), which is different from the original point unless \( k = 0 \). Reflecting it across the \( y \)-axis keeps the \( y \)-coordinate the same, but flips the \( x \)-coordinate, giving you \( (0, k) \) again, which is a win! Similarly, reflections across the lines \( y=x \) and \( y=-x \) change the coordinates and won’t return the point to its original position. In the realm of reflections, the only way to keep your coordinates \( (0, k) \) intact is to reflect across the \( y \)-axis! It’s like taking a mirror selfie with the \( y \)-axis—there’s no change as long as you’re sticking to that vertical buddy! So, there you have it, it’s all about choosing the right axis to maintain your original spot!