Triangle abc is translated onto its image, triangle a'b'c'. use the given vertices of the triangles to answer parts a and b. a(-6, 0) b(-1, 0) c(-5, 3) a'(-2, 4) b'(3, 4) c'(-1, 7) part a: use the distance formula to prove that the translation was an isometric transformation. include all of your work in your final answer. part b: use complete sentences to describe the translation that maps triangle abc onto its image.

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.