Final answer:
To find the perimeter of a parallelogram with given coordinates, we can use the distance formula to find the length of one side and then multiply it by 4.
Step-by-step explanation:
To find the perimeter of a parallelogram, we need to find the lengths of all its sides and then add them together. In this case, we have the coordinates A(-4,3) and B(1,5). Using the distance formula, we can find the length of side AB. The distance formula is:
d = sqrt((x2-x1)^2 + (y2-y1)^2)
Plugging in the values:
d = sqrt((1-(-4))^2 + (5-3)^2)
d = sqrt((5)^2 + (2)^2) = sqrt(25 + 4) = sqrt(29).
Therefore, the length of side AB is sqrt(29). Since a parallelogram has opposite sides equal in length, the perimeter of the parallelogram is 2 * sqrt(29) + 2 * sqrt(29) = 4 * sqrt(29).