1. Transformations As Functions
~ Adapted from Walch Education

2. Transformations
A transformation changes the position, shape, or size of a figure on a coordinate plane.
The original figure, called a preimage, is changed or moved, and the resulting figure is called an image.

3. An isometry is a transformation in which the preimage and the image are congruent.
An isometry is also referred to as a “rigid transformation” because the shape still has the same size, area, angles, and line lengths.

4. Figures are congruent if they both have the same shape, size, lines, and angles. The new image is simply moving to a new location.
T(x, y) = (x + h, y + k), then would be:

5. ONE-TO-ONE
Transformations are one-to-one, which means each point in the set of points will be mapped to exactly one other point and no other point will be mapped to that point.

6. More Info…
The simplest transformation is the identity function I where I: (x', y' ) = (x, y).
Transformations can be combined to form a new transformation that will be a new function.

7. Because the order in which functions are taken can affect the output, we always take functions in a specific order, working from the inside out.
For example, if we are given the set of functions h(g(f(x))), we would take f(x) first and then g and finally h.

8. Three Isometric Transformations
A translation, or slide, is a transformation that moves each point of a figure the same distance in the same direction.
A reflection, or flip, is a transformation where a mirror image is created.
A rotation, or turn, is a transformation that turns a figure around a point.

9. Some transformations are not isometric
Some transformations are not isometric. Examples of non-isometric transformations are horizontal stretch and dilation.
A dilation stretches or contracts both coordinates.

10. Practice #1
Given the point P(5, 3) and T(x, y) = (x + 2, y + 2), what are the coordinates of T(P)?
T(P) = (x + 2, y + 2)
(5 + 2, 3 + 2)
(7, 5)
T(P) = (7, 5)

11. Challenge Problem Given the transformation of a translation
T5, –3, and the points P (–2, 1) and Q (4, 1), show that the transformation of a translation is isometric by calculating the distances, or lengths, of and

12. Thanks for Watching!!!
~Ms. Dambreville