1. 1.4 Rigid Motion in a plane Warm Up
Use the points G(-3, -7) and H(2, -3) to answer the following:
1. Find the slope of 𝐺𝐻 Find the midpoint of 𝐺𝐻
3. Find GH

2. 1.4 Transformations
Objectives
Identify reflections, rotations, and translations.
Graph transformations in the coordinate plane.

3. Transformation – a change in the ___________, _________ , or _________ of a figure.
Rigid Transformation – a change in the position of a figure that does not change its _______________ or ________________.
Preimage – the __________ figure in a transformation.
Image – the _____________ figure in a transformation.
Isometry – a transformation in which the original figure and its image are ___________.
size
shape
position
size
shape
original
resulting
congruent

4. A transformation maps the preimage to the image
A transformation maps the preimage to the image. Arrow notation () is used to describe a transformation, and primes (’) are used to label the image.

5. Three Rigid Transformations
Reflection (flip)
Rotation (turn)
Translation (slide)
A transformation across a line, called the line of reflection. Each point and its image are the same distance from the line of reflection.
A transformation about a point P, called the center of rotation. Each point and its image are the same distance from P.
A transformation in which all the points of a figure move the same distance in the same direction.

6. Example 1
Identify the transformation. Then use arrow notation to describe the transformation.
A. B. C.

7. Example 2
Name the transformation.
ABC A’B’C’
A’B’C’ A”B”C”

8. B C D A K N M L Example 3 Use the picture to answer the following:
Figure ABCD Figure ________
Name and describe the transformation.
Name the image of 𝐴𝐷 .
Name the preimage of 𝐿𝑀 .
Name the coordinates of the image of B. B C D A K N M L

9. Example 4
Show that the transformation is an isometry by using the Distance Formula to compare the side lengths of the triangles.

10. Find the value of each variable given that the transformation
Example 5
Find the value of each variable given that the transformation
is an isometry.
3x – 8 7
3y°
45°
2z + 13 25