Answer:
(-5, -2)
Step-by-step explanation:
Each reflection puts the image point as far from the axis on the other side as the original is from the axis. The designated axis is the perpendicular bisector of the segment joining the point and its image.
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The coordinates of the image can be found analytically (as follows), or by plotting the points on a graph (see attachment).
Reflection across the x-axis changes the sign of the y-coordinate. The point remains on the same vertical line, so its x-coordinate is unchanged:
(x, y) ⇒ (x, -y) . . . . . . reflection across the x-axis
(5, 2) ⇒ (5, -2) . . . . point after first reflection
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Reflection across the y-axis changes the sign of the x-coordinate. The point remains on the same horizontal line, so its y-coordinate is unchanged:
(x, y) ⇒ (-x, y) . . . . . . reflection across the y-axis
(5, -2) ⇒ (-5, -2) . . . . point after second reflection
The image point after reflection across both axes is (-5, -2).
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Additional comment
Effectively, reflection across both axes changes the signs of both coordinates. It is fully equivalent to reflection across the origin, or rotation 180° about the origin.
The combination of the two reflections is ...
(x, y) ⇒ (-x, -y) . . . . . reflection in x- and y-axes, the origin, or rotation 180°
