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Part A:
An isometric transformation is a type of transformation where the original shape and size of the pre-image is not altered in the image.
To show that the translation was an isometric transformation, we show that the distance between any two points in the pre-image is equal to the distance between the corresponding points in the image.
Consuder, line AB, the distance between point A and point B is given by:
The distance between point A' and point B' in the image is given by:
Similarly checking other points of the pre-image against the corresponding points of the image shows that the size of the pre-image is preserved in the image.
Part 2:
The translation that maps the triangle ABC onto its image are:
Triangle ABC was shifted 4 units to the right.
Triangle ABC was shifted 4 units up.
An isometric transformation is a type of transformation where the original shape and size of the pre-image is not altered in the image.
To show that the translation was an isometric transformation, we show that the distance between any two points in the pre-image is equal to the distance between the corresponding points in the image.
Consuder, line AB, the distance between point A and point B is given by:
The distance between point A' and point B' in the image is given by:
Similarly checking other points of the pre-image against the corresponding points of the image shows that the size of the pre-image is preserved in the image.
Part 2:
The translation that maps the triangle ABC onto its image are:
Triangle ABC was shifted 4 units to the right.
Triangle ABC was shifted 4 units up.