Translations Advanced Geometry Rigid Transformations Lesson 1

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

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

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

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

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.

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

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?

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

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

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.

Using a Protractor