A double reflection of a preimage across perpendicular lines produce the same result as a:
rotation of the preimage.
rotational symmetry of order 2.
rotation of 180 degrees around the point of intersection of the two lines.
To understand this conceptually, imagine a preimage (an object or shape) on a coordinate plane. If we first reflect this preimage across one perpendicular line, the image produced will be the mirror reflection of the original preimage. Then, if we reflect this new image across the second perpendicular line, it will again undergo a mirror reflection. This double reflection essentially flips the preimage twice, resulting in the same orientation as the original preimage.
Alternatively, we can think of this process analytically. Let's assume the two perpendicular lines intersect at the origin, (0,0), on a Cartesian coordinate plane. Suppose the coordinates of a point on the preimage are (x,y). The first reflection across one of the lines can be achieved by taking the negative of the x-coordinate, (-x,y), which flips the preimage across the vertical line. The second reflection across the other perpendicular line can be achieved by taking the negative of the y-coordinate, (-x,-y), flipping the preimage across the horizontal line.
Combining these two reflections, we end up with the coordinates (-x,-y), which is equivalent to rotating the preimage 180 degrees around the origin. Hence, the double reflection across perpendicular lines produces the same result as a rotation of 180 degrees around the point of intersection of the two lines.