Advanced Geometry Rigid Transformations Lesson 1

1. Translations Advanced Geometry Rigid Transformations Lesson 1

2. Terminology Transformation Definition - the movement of a figure in a plane from its original position to a new position Rigid transformation does not change the size or shape of the figure congruence transformation isometry

3. Terminology Pre-image Definition – a figure that undergoes a motion or transformation Image Definition – a figure that results from a transformation of a figure

4. Translation Slide all points of a figure the same __________ in the same __________. distance direction Rectangle ABCD was translated 5 units right and 2 units up.

5. Notation Coordinate Form Rectangle ABCD was translated 5 units right and 2 units up. 5 units right x + 5 y + 2 2 units up (x, y)  (x + 5, y + 2)

6. Example: Quadrilateral HJLK has vertices H(-1, 0), J(0, 2), L(3, 1), and K(2, -2) is translated by (x, y)  (x – 3, y + 3). Graph HJLK and its image. List the coordinates of the image.

7. Example: Find the translation that moves each figure on the coordinate plane. Write the translation as a sentence and in coordinate form.

8. Example: Triangle TUV is translated 3 units up and 5 units left to create ∆T’U’V’ with vertices T’(-6, -1), U’(1, 5), and V’(0, -2). What are the coordinates of the vertices of ∆TUV?

9. Terminology Translations are congruence transformations, or isometries. They preserve: • distance (length of segments) • angle measures • betweenness of points • collinearity

10. Discussion Triangle ABC is translated to ∆DEF . Compare and contrast the figures.

11. A transformation made up of successive transformations is called a _______________. composition Example: Rectangle MNPQ with vertices M(-3, -1), N(1, -1), P(1, 4), and Q(-3, 4) is translated down 4 and right 6 units. That image is then translated up 3 and left 7 units. Write the coordinate form of each translation and then the composition.

12. Using a Protractor