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.
Answer:
C. The data are qualitative because they don't measure or count anything.
Step-by-step explanation:
Quantitative data is about numbers or counts. For example, the number of children of a couple is an example of quantitative data.
Qualitative data is about characteristics, when they don't count or measure anything. For example, if my favorite kind of movie is comedy, for example, it is an example of qualitative data. There are no counts or measurements.
So the correct answer is:
C. The data are qualitative because they don't measure or count anything.
Answer:
25
Step-by-step explanation:
5 > x/5
5 × 5 > (x/5) × 5
25 > x
The answer would be B. 2 times the X number minus 2 would be the Y for each.