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.
1,132 people came to watch the balloon festival.
<span>This time we slice the cube corner first. The sequence begins with a triangle, and as the slice passes three corners of the cube, the triangle becomes cut off. The triangle becomes more cut off and eventually becomes a perfect hexagon. The sequence continues by becoming a triangle again as it passes the next three vertices, then shrinks to a point. This is seen most clearly in the second slicing sequence which shows a symmetric set of slices starting at the back-most vertex. The first set of slices start at one of the side vertices, and in this sequence, the triaganles and hexagons do not seem to be regular due to the fact that they are tilted with respect to our line of sight. These two sequences represent all the possibilities for the orthographic view.
</span><span>Here we slice the cube edge first. Slices are taken in two directions. The first is from the left vertical edge. In the orthographic view, this appears as a line since the slicing plane is parallel to our viewing direction. The second slicing sequence starts at the lower, back, left-hand edge. This one appears as a thin rectangle which thickens, achieving its widest point half-way through, then shrinks back to an edge. Every edge in the orthographic view is symmetric to one of these two edges, so we have seen every important slicing sequence.</span>
Answer is <span>A. y=14x
hope that helps</span>