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Geometric Transformations Summary

Learn about translations, reflections, rotations, and dilations in geometry with examples and explanations. Understand how figures maintain size, shape, and orientation through various transformations.

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Geometric Transformations Summary

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  1. Translations Translations maintain Same Size Same Shape Same Orientation A’ A B’ C’ B C ∆ABC → ∆A’B’C’ A → A’ B → B’ C → C’ y + 2 (x,y) x + 6 ( x, y ) → ( x + 6, y + 2 ) ( - 3,1) → ( - 3 + 6, 1 + 2 ) B B’ ( 3, 3)

  2. Translations Translations maintain Same Size Same Shape Same Orientation A’ A B’ C’ B C ∆ABC → ∆A’B’C’ A → A’ B → B’ C → C’ x + 8 (x,y) y – 5 ( x, y ) → ( x + 8, y – 5 ) ( - 5,4) → ( - 5 + 8, 4 – 5 ) A A’ ( 3, -1)

  3. Reflections Reflections maintain Same Size Same Shape Reflection is over a line The Orientation of the new image is a mirror image of the original A (-3,4) A’ (3,4) • • • B (-3,1) C (-1,1) C’ (1,1) B’ (3,1) Reflection over the y-axis Any point, A, reflected over a line to A’ is the same distance on the opposite side of the line

  4. Reflections Reflections maintain Same Size Same Shape Reflection is over a line The Orientation of the new image is a mirror image of the original A (-3,4) • Reflection over the x-axis Any point, A, reflected over a line to A’ is the same distance on the opposite side of the line • • C (-1,1) B (-3,1) C’ (-1,-1) B’ (-3,-1) A’ (-3,-4)

  5. Reflections Reflections maintain Same Size Same Shape Reflection is over a line The Orientation of the new image is a mirror image of the original A (-3,4) • Reflection over the line y = x Any point, A, reflected over a line to A’ is the same distance on the opposite side of the line • • C (-1,1) B (-3,1) C’ (1,-1) B’ (1, -3) A’ (4, -3)

  6. Rotations Rotations maintain Same Size Same Shape Rotation is around a point A’ and A are both the same distance from center of rotation. A (-5,4) • • • 90° counter-clockwise rotation about the origin Positive 90° B (-5,1) C (-3,1) C’ (-1, -3) A’ (-4, -5) B’ (-1, -5)

  7. Rotations Rotations maintain Same Size Same Shape Rotation is around a point A’ and A are both the same distance from center of rotation. B’ (1, 5) A’ (4, 5) A (-5,4) • C’ (1, 3) • • B (-5,1) C (-3,1) 90° clockwise rotation about the origin Negative 90°

  8. Rotations Rotations maintain Same Size Same Shape Rotation is around a point A’ and A are both the same distance from center of rotation. A (-5,4) • 180° counter-clockwise rotation about the origin Positive 180° • • B (-5,1) C (-3,1) C’ (3, -1) B’ (5, -1) A’ (5, -4)

  9. Dilation A Dilation causes a change in size but not a change in shape. The points move along lines drawn from the center of dilation through the original points. The scale factor is the ratio of a side of the new figure to the corresponding side of the original figure. A (4, 8) A (2, 4) • B (4, 2) C (8, 2) • • B (2, 1) C (4, 1) • Dilation with the Center at the origin and a scale factor of 2

  10. Dilation A Dilation causes a change in size but not a change in shape. The points move along lines drawn from the center of dilation through the original points. The scale factor is the ratio of a side of the new figure to the corresponding side of the original figure. A (3, 6) • A’ (2, 4) B (3, 3) • • C (9, 3) B ‘(2, 2) C (6, 2) • Dilation with the Center at the origin and a scale factor of 2 / 3.

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