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.
Accepted Solution
A:
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:
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.