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Reflections in the x-y Plane

The content provides an in-depth exploration of the concept of reflections in the x-y plane, focusing on how points are reflected over the x-axis, y-axis, and specific lines y = x and y = -x, and the geometric principles underlying these reflections.
  • Reflections over the x-axis and y-axis involve flipping the sign of the y-coordinate or x-coordinate, respectively, while maintaining the same absolute value.
  • Reflecting a point over the line y = x results in the x- and y-coordinates being switched.
  • Reflecting a point over the line y = -x involves switching the x- and y-coordinates and changing their signs.
  • A key geometric principle is that the line of reflection acts as the perpendicular bisector of the segment connecting the original point and its reflection, and any point on this line is equidistant from both the original and reflected points.
  • These concepts are crucial for solving advanced questions on reflections in the GRE exam.
Introduction to Reflections
Reflections Over the x-axis and y-axis
Reflections Over the Line y = x
Reflections Over the Line y = -x
Summary of Reflection Principles