Question

journal
determine whether each
statement is true or false. if the
statement is false, rewrite it so
that it becomes a true statement.
1 a translation function along
parallel lines is a type of
geometric transformation
that is non - rigid.
2 isometries include geometric transformations such as translations,
rotations, and reflections.
3 a transformation is an isometry when it does not preserve size
and shape.
4 a dilation is a non - rigid geometric transformation.
remember
a translation is a function, t, which takes as its input a set
of pre - image points and outputs a set of image points.
you translate the pre - image points a distance of ab in the
direction ab. for example, you can express a translation
of point p as (t_{ab}(p)) or (p).
practice
1 write a function to describe each translation. each solid figure is a pre - image, and each
dashed figure is an image.
(a) image of a rectangle pre - image and a dashed rectangle image with points a and b
(b) image of a trapezoid pre - image and a dashed trapezoid image with points a and b
(c) image of a hexagon pre - image and a dashed hexagon image with points p and q
(d) image of a triangle pre - image and a dashed triangle image with points p and q

Explanation:

Step1: Analyze Statement 1

A translation (along parallel lines) is a rigid transformation because it preserves the size and shape of the figure. So the statement "non - rigid" is wrong. Rewrite: A translation function along parallel lines is a type of geometric transformation that is rigid.

Step2: Analyze Statement 2

Isometries are transformations that preserve distance (and thus size and shape). Translations, rotations, and reflections all preserve distance, so they are isometries. This statement is true.

Step3: Analyze Statement 3

An isometry is a transformation that preserves size and shape (distance). The statement says "does not preserve", so it's wrong. Rewrite: A transformation is an isometry when it preserves size and shape.

Step4: Analyze Statement 4

Dilation changes the size of the figure (scales it) while preserving the shape, so it is a non - rigid transformation. This statement is true.

Answer:

1. False; A translation function along parallel lines is a type of geometric transformation that is rigid.
2. True
3. False; A transformation is an isometry when it preserves size and shape.
4. True