Answer:
The value of a = 14
Step-by-step explanation:
Given
(x₁, y₁) = (2, 4)
(x₂, y₂) = (6, a)
(x₃, y₃) = (-1, 1)
A = 9 sq.units
Area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:

substituting the values (x₁, y₁) = (2, 4), (x₂, y₂) = (6, a), (x₃, y₃) = (-1, 1), A = 9 in th formula


Multiply both sides by 2

simplify

As the area is always positive.
so


Add 18 to both sides

simplify



Divide both sides by 3


Thus, the value of a = 14
The product is 18n^2-48n-12n+32 which simplifies to 18n^2-60n+32. I got this using the FOIL method (First, Outer, Inner, Last)
The answer to your question is 11,474
(X,Y-4) this is the answer to the question since the y value of the translated image is moved down from the preimage