Final answer:
To show that the points form a parallelogram, we check if the slopes of opposite sides are equal. The length of the diagonals can be found using the distance formula.
Step-by-step explanation:
To show that the points (2, 0), (5, -1), (11, 4), and (8, 5) are the vertices of a parallelogram, we can calculate the slopes of opposite sides and check if they are equal. The slope of the line passing through (2, 0) and (5, -1) is -1/3. The slope of the line passing through (11, 4) and (8, 5) is -1/3 as well. Since the slopes of opposite sides are equal, the points form a parallelogram.
To find the length of the diagonals, we can use the distance formula. The length of the diagonal connecting (2, 0) and (11, 4) is sqrt((11 - 2)^2 + (4 - 0)^2) = sqrt(81 + 16) = sqrt(97).
The length of the diagonal connecting (5, -1) and (8, 5) is sqrt((8 - 5)^2 + (5 - (-1))^2) = sqrt(9 + 36) = sqrt(45).