Final answer:
The area of Triangle ABC remains the same after being translated 3 units upward because translations do not change the size or shape of geometric figures.
Step-by-step explanation:
When Triangle ABC is translated 3 units upward, the area of the triangle remains the same. A translation is a type of transformation that slides a figure in any direction without changing its size, shape, or orientation. Therefore, moving a triangle up or down or to the side does not alter the amount of space it encloses, and consequently, its area stays constant.
To support this concept with an example related to areas, consider a square with a side length of 4 inches. If we translate it in any direction, the area remains 16 square inches because translations do not affect dimensions. Similarly, if Triangle ABC is translated, its area remains unaffected.
The areas A₁, A₂, and A₃ are all the same according to the options provided, which is represented as option (b) A₁ = A₂ = A₃, since their areas are determined by their dimensions, not their positions in the plane.