Final answer:
The parallelogram formed by the given points is a Rhombus.
Step-by-step explanation:
To determine the type of parallelogram created by the given points, we need to check if the opposite sides of the parallelogram are parallel and equal in length. Let's calculate the slopes of the lines created by the given points:
Line AB: slope = (4 - 2) / (4 - (-1)) = 2 / 5
Line CD: slope = (-3 - 2) / (-3 - 4) = -5 / -7 = 5 / 7
Line BC: slope = (2 - 4) / (-1 - 4) = -2 / -5 = 2 / 5 (same as the slope of line AB)
Line DA: slope = (-1 - (-3)) / (2 - (-3)) = 2 / 5 (same as the slope of line CD)
Since opposite sides have the same slopes, we can conclude that the given points form a parallelogram. To determine the type of parallelogram, we need to check if the consecutive sides are equal in length.
Distance AB = sqrt((4 - 2)^2 + (4 - (-1))^2) = sqrt(4 + 25) = sqrt(29)
Distance CD = sqrt((-3 - 2)^2 + (-3 - 4)^2) = sqrt(25 + 49) = sqrt(74)
Distance BC = sqrt((2 - 4)^2 + (-1 - 4)^2) = sqrt(4 + 25) = sqrt(29) (same as the distance AB)
Distance DA = sqrt((-1 - (-3))^2 + (2 - (-3))^2) = sqrt(4 + 25) = sqrt(29) (same as the distance CD)
Since opposite sides are equal in length, we can conclude that the parallelogram formed by the given points is a Rhombus.