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Reflections in Mathematics

Learn about reflections in geometry - a transformation that reflects every point in a figure over a given line. Discover the properties of reflection, how to reflect across axes, and practice reflecting points in the coordinate plane. Understand how reflections preserve size and shape while changing orientation.

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Reflections in Mathematics

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  1. Reflections A reflection is a transformation that reflects every point in a figure over a given line. After reflection, the image of the figure is congruent to the preimage, but has a different orientation.

  2. Property of reflection • A reflection is an isometry, meaning the preimage and its reflected image have the same size and shape.

  3. To reflect a point across a horizontal or vertical line, imagine that the line is a mirror, and visualize the reflected location of the point.

  4. Reflecting across an axis • Reflect tri ABC across the y-axis • Imagine each point reflected across a mirror sitting on the y-axis. When a point is reflected across the y-axis , its y-coordinate does not change

  5. Reflecting across a horizontal line • Reflect tri ABC across the x-axis • Notice that when a point is reflected across a horizontal line, its x-coordinate does not change

  6. Reflecting across a line • To find the reflection of a point across any line in the coordinate plane, draw a perpendicular line from the point to the line of reflection. The point's reflection will be equidistant from the line of reflection on both sides

  7. practice • Rectangle ABCD has vertices at A(1,1), B(5.5,1), C(5.5,3.5), D(1,3.5) • Reflect ABCD across the y-axis • Reflect ABCD across the line y = 2 • Reflect ABCD across the line y =x

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