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Geometry with McCarthy

In this section, we explore the concept of reflections in geometry, a key transformation that maps figures across lines. You will learn how to identify and accurately draw reflections using coordinate points and lines of reflection in the coordinate plane. We will cover reflections across the x-axis, y-axis, and the line y = x, providing detailed examples for each. Additionally, you will understand isometries and how they maintain the shape and size of figures. Master these concepts to enhance your geometric understanding.

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Geometry with McCarthy

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  1. Geometry with McCarthy Section 9-1: Reflections

  2. What you’ll learn Objectives: Identify and draw reflections.

  3. Identifying Reflections A reflection is a transformation that moves a figure across a line.

  4. Not a reflection

  5. Line of reflection Line of reflection

  6. Reflections in the coordinate plane P(x, y) P(x, y) P’(-x, y) P(x, y) P’(y, x) P’(x, -y) Across the x-axis Across the y-axis Across the line y=x (x, y)  (x, -y) (x, y)  (-x, y) (x, y)  (y, x)

  7. Example Reflect the figure with the given vertices across the given line. M(1, 2), N(1, 4), P(3, 3); y-axis D(2, 0), E(2, 2), F(5, 2), G(5, 1); y=x

  8. Isometry An isometryis a transformation that does not change the shape or size of a figure.

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