Which statement about the transformation is true it is rigid because?

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations".

A reflection over line m (notation rm ) is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the reflection line as the original point, but is on the opposite side of the line. A reflection is called a rigid transformation or isometry because the image is the same size and shape as the pre-image.

In this reflection that maps ΔABC to ΔA'B'C', the distances from the pre-image points to the image points vary (are not necessarily equal), but the segments representing these distances are parallel.

Orientation (lettering): The lettering of the points of the

Properties preserved under a line reflection from the pre-image to the image.
1. distance (lengths of segments remain the same)
2. angle measures (remain the same)
3. parallelism (parallel lines remain parallel)
4. collinearity (points remain on the same lines)
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The orientation (lettering around the outside of the figure), is not preserved. The order of the lettering in a reflection is reversed (from clockwise to counterclockwise or vice versa).

A reflection is a rigid transformation (isometry) that maps every point P in the plane to point P', across a line of reflection, m, such that:

A translation (notation Ta,b ) is a transformation which "slides" a figure a fixed distance in a given direction. In a translation, ALL of the points move the same distance in the same direction.
A translation is called a rigid transformation or isometry because the image is the same size and shape as the pre-image.

In this translation that maps ΔABC to ΔA'B'C', the distances from the pre-image points to the image points are equal, and the segments representing these distances are parallel.

Orientation (lettering): The lettering of the points of the

Properties preserved under a translation from the pre-image to the image.
1. distance (lengths of segments remain the same)
2. angle measures (remain the same)
3. parallelism (parallel lines remain parallel)
4. collinearity (points remain on the same lines)
5. orientation (lettering order remains the same)

A translation is a rigid transformation of the plane that moves every point of a pre-image a constant distance in a specified direction.

mapping:
Example:   
 (x, y) → (x + 8, y - 6)

Read: "the x and y coordinates are mapped to x + 8 and y - 6 respectively".

notations:
Example:    T8,-6    or
T8,-6 (x, y) = (x + 8, y - 6)
The 8 tells you to "add 8" to all x-coordinates, while the -6 tells you to "subtract 6" from all of the y-coordinates.

description:
Example:
"8 units to the right and 6 units down."

A verbal or written description of the translation is given.

Movement: Remember that adding a negative value (subtracting), indicates movement left and/or down, while adding a positive value indicates movement right and/or up.

Using vectors to show movement of a translation:

A vector is represented by a directed line segment, a segment with an arrow at one end indicating the direction of movement. Unlike a ray, a directed line segment has a specific length. The Pythagorean Theorem can be used to find the length of a vector in the coordinate plane.

Vectors used in translations are what are known as "free vectors", which are a set of parallel directed line segments. A vector translation moving "8 units to the right and 6 units down" can be written as

In this rotation that maps ΔABC to ΔA'B'C', the distances from the pre-image points to the image points vary (as they are the radii of the circles). Unlike reflections and translations, the segments connecting pre-image and image points are NOT parallel.

Orientation (lettering): The lettering of the points of the pre-image, in this diagram, is counterclockwise A-B-C, and the image is also lettered counterclockwise A'-B'-C'.

Properties preserved under a rotation from the pre-image to the image.
1. distance (lengths of segments remain the same)
2. angle measures (remain the same)
3. parallelism (parallel lines remain parallel)
4. collinearity (points remain on the same lines)
5. orientation (lettering order remains the same)

Common Graph Rotations:
(center at the origin, O)

There are two possible directions to travel when rotating.

Look at point P in the diagram at the right. The positive x-axis is considered the "starting" location of 0º. You can have an angle of rotation of positive 135º counterclockwise to point P, or a negative angle of 225º clockwise to point P.
Notice that together, the angles (135º and 225º) form a complete circle (360º).

It is even possible to have one complete revolution (360º) PLUS and additional 135º to get to P (an angle of rotation of 495º).

When working in the coordinate plane, it is important to have a visual understanding of how the quadrants are divided through rotational angles. The most common angles seen on the grid are multiples of 15º. The "favorite" angles are usually 30º, 45º, 60º, 90º, 180º, and 270º.

There is an "identity" rotational transformation of 0º that maps all points onto themselves (no movement of the pre-image), written RC,0 (P) = P. (You may also see the identity transformation denoted by the letter I.)