Q1.
Question
Compare and contrast the size and shape of the pre-image and image for each type of transformation. Tell which transformations are isometries.
Step-by-Step Solution
Verified- In translation shape and size does not change. It is isometry.
- In dilation shape does not change but size changes. It is not isometry.
- In reflection shape and size does not change. It is isometry.
- In rotation shape and size does not change. It is isometry.
If image and pre-image are congruent figures then transformation is isometry.
A translation occurs when figure is moved from one location to another location without changing its size shape or orientation.
As size shape or orientation does not change, so image and pre-image are congruent figures thus translation is isometry.
A dilation occurs when figure is reduced or enlarged.
As size changes so image and pre-image are not congruent figures. Thus it is not isometry.
A reflection occurs when every point of a figure is mapped to a corresponding image across a line of symmetry.
As reflection does not change shape and size, so image and pre-image are congruent figures. Thus it is isometry.
A rotation occurs when a figure is moved around a centre point, usually origin.
As rotation does not change shape and size, so image and pre-image are congruent figures. Thus it is isometry.