1. Transformations
By: Christina Chaidez
Math 1351

2. 1st Grade TEKS 111.3 Mathematics
Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties.
1st Grade

3. TEKS continued..
identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language;
identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language;
compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible;
partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words; and

4. Transformation
Any function from a plane to itself that is one-to-one correspondence is a transformation of a plane.
Any transformation of a plane that preserves distance is an isometry (motion).
Translations
Reflections
Rotations

5. Transformation example
Transformation involves moving an object from its original position to a new position. The object in the new position is called the image. Each point in the object is mapped to another point in the image.
The original object is ABC and the image is A’B’C’

6. interactive transformed figure

7. Translation (slide)
is a (motion) or transformation of a plane that moves every point of the plane a specified distance in a specified direction along a straight line. The translation is determined by:
Slide arrow
Vector
Slide line

8. Translation Example
Figure J is the pre image and figure S is the translated image.
A translation is a function from the plane to plane such that the image of the point coordinates (x,y) is (x+a, y+b), where a and b are real numbers.

9. interactive translated figure
In Geometry, "Translation" simply means Moving ...
... without rotating, resizing or anything else, just moving.

10. Reflection
In line is a transformation from the plane to the plane that every point is the same distance from the central line and the reflection has the same size as the original image.
The central line is called the Mirror Line

11. Reflection example
Students can fold a paper along the reflecting line and by drawing the image on the other side gives the mirror image.

12. interactive reflected figure
Every point on the line segment AB is "reflected" in the mirror and appears on the other side of the line an equal distance from it.

13. Rotation (turn)
A transformation of the plane determined by holding one point, the turn center, fixed and rotating the plane about this point by a certain amount in a certain direction.

14. Rotation example
The coordinates of Pentagon ABCDE are: (0,4); (7,4); (9,2); (7,0); (0,0)
Pentagon ABCDE is rotated 180° about the origin making the coordinates of Pentagon A1B1C1D1E1:
(0,-4); (-7,-4); (-9,-2); (-7,0); (0,0)

15. interactive rotated figure