Explanation:
I am not sure I understand everything you have to do here.
what I see is a parallelogram (right ?), where we need to find the coordinates of C.
then we need the length of AB (right ?).
and the area of ABCD (right ?).
and the perimeter of ABCD (right ?).
I base the following on these assumptions above.
since it is a parallelogram, it has 2 pairs of equally long and parallel sides (top and bottom, and left and right).
the opposite angles are equal (top left and bottom right, bottom left and top right).
that means, every shift that was done to get B or if A, had to be done also to get C or if D.
to get B out of A, the following shift was applied :
(2, 0) + (3 - 2, 4 - 0) = (2, 0) + (1, 4) = (3, 4)
to get C we need to do the same thing to D :
C = (-2, 0) + (1, 4) = (-1, 4)
the length of AB (= length of DC) is calculated via Pythagoras by using the coordinate differences of the 2 end points as legs and the actual distance as Hypotenuse of the corresponding right-angled triangle :
length² = (3-2)² + (4-0)² = 1² + 4² = 1 + 16 = 17
length AB = length DC = sqrt(17) units =
= 4.123105626... units
to get the area and the perimeter of the parallelogram we also need the length of DA (= length of CB).
that is easy, as they are horizontal, but just to be clear and consistent, we use the same method again :
length² = (2 - -2)² + (0 - 0)² = 4² + 0² = 16
length DA = length CB = sqrt(16) = 4 units
the perimeter of ABCD is then
2×4 + 2×sqrt(17) = 8 + 2×sqrt(17) units =
= 16.24621125... units
the area of a parallelogram is
baseline × height
so we need the height (direct, right-angled distance of the top line from the bottom line).
that is in our case (top and bottom lines are horizontal) simply the y-coordinate difference between A and B (= y-coordinate difference between D and C) :
4 - 0 = 4 units
so, the area of our parallelogram here is
baseline × height = 4×4 = 16 units²