Final answer:
The line of reflection that maps point K to point K' at (-5, 2) is the y-axis. This is because the y-coordinate remains unchanged, while the x-coordinate is inverted.
Step-by-step explanation:
The student has asked about the line of reflection that maps point K to point K' at (-5, 2). To determine the correct line of reflection, we can examine the possible options:
The x-axis reflection would result in a point with the same x-coordinate and an inverted y-coordinate, i.e., if K is at (x, y), K' would be at (x, -y).The y-axis reflection would result in a point with the same y-coordinate and an inverted x-coordinate, i.e., if K is at (x, y), K' would be at (-x, y).A reflection over the line y = x would swap the coordinates of the point, so if K is at (x, y), K' would be at (y, x).A reflection over the line y = -x would result in a point where both coordinates are swapped and negated, so if K is at (x, y), K' would be at (-y, -x).
In the case of point K being reflected to point K' at (-5, 2), the reflection that corresponds to this transformation is a reflection over the y-axis, as the y-coordinate remains the same while the x-coordinate is negated.
Therefore, the correct answer is b. y-axis.