**Reflections in the x-y Plane**

Summary

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 such as y = x and y = -x. It elucidates the geometric principles underlying these reflections, emphasizing the role of the mirror line as the perpendicular bisector and its equidistance from the original and reflected points.

- Reflections over the x-axis and y-axis involve maintaining the same x or y-coordinate, respectively, while inverting the sign of the other coordinate.
- Reflecting a point over the line y = x results in switching the x- and y-coordinates, whereas reflecting over y = -x switches and inverts the sign of both coordinates.
- The mirror line acts as a perpendicular bisector of the segment connecting the original point and its reflection, with every point on the mirror line being equidistant from both.
- Understanding these principles simplifies the approach to solving advanced GMAT questions involving point reflections.
- Practical examples and a practice question illustrate how to apply these concepts to solve reflection problems on the GMAT.

Chapters

00:00

Introduction to Reflections

01:18

Reflections Over the X and Y Axes

02:36

Reflections Over the Line y = x

05:38

Reflections Over the Line y = -x

08:39

Summary of Reflection Principles

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