Honors Geometry Transformations Section 1 Reflections

1. Honors Geometry Transformations Section 1Reflections

2. A transformation is a movement of a figure in a plane from its original position to a new position.

3. The original figure is called the , while the figure resulting from the transformation is called the . A point in the image is usually named by adding a prime symbol (  ) to the name of the point in the preimage. preimage image

4. In a rigid transformation, or isometry, the image is congruent to the preimage.

5. We will consider three basic isometries: translations, reflectionsand rotations.

6. A reflection in a line m (or flip over line m) is a transformation that maps (or matches up) any point P to a point so that these two properties are true.1. If P is not on m, then2. If P is on m, then

8. Let’s take a look at reflections in the coordinate plane.

9. Example 1: Consider reflecting point A(3, 5) in the given line. Give the coordinate of its image.Aa) x-axis ________b) y-axis ________c) the line y = 1 _______d) the line x = -2 ________

10. e) the line y = x _______ f) the line y=-x+2 _____g) the line y = x - 1 _____

11. e) the line y = x _______ f) the line y=-x+2 _____g) the line y = x - 1 _____

12. A figure has a line of symmetry if the figure can be mapped onto itself by a reflection in a line.

13. The previous statement is the formal definition of a line of symmetry, but it is much easier to think of a line of symmetry as the line where the figure can be folded and have the two halves match exactly.

14. Example 2: Draw all lines of symmetry.

15. Example 3: Name two capital letters that have exactly two lines of symmetry.