Answer:
Based on the given points, the figure is not a parallelogram, since opposite sides are not parallel or do not have equal length.
Explanation:
To determine if a figure is a parallelogram using the given points, we need to check whether the opposite sides are parallel and have equal length. We can use the distance formula and slope formula to calculate the length and slope of each side.
Using the distance formula, we can calculate the lengths of the sides:
ST = sqrt((10-1)^2 + (7-5)^2) = sqrt(89)
TU = sqrt((14-10)^2 + (1-7)^2) = 6sqrt(2)
UV = sqrt(((-3)-14)^2 + ((-1)-1)^2) = 5sqrt(2)
VS = sqrt((2-(-3))^2 + ((-3)-5)^2) = sqrt(89)
PQ = sqrt((6-(-4))^2 + (4-2)^2) = 2sqrt(17)
QR = sqrt((11-6)^2 + ((-2)-4)^2) = sqrt(61)
RP = sqrt((11-(-4))^2 + ((-2)-2)^2) = 5sqrt(2)
PS = sqrt((2-(-4))^2 + ((-3)-2)^2) = 5
Using the slope formula, we can calculate the slopes of the sides:
ST: slope = (7-5)/(10-1) = 2/9
TU: slope = (1-7)/(14-10) = -3/2
UV: slope = ((-1)-1)/((-3)-14) = 2/17
VS: slope = (-3-5)/(2-(-3)) = -2/5
PQ: slope = (4-2)/(6-(-4)) = 1/5
QR: slope = ((-2)-4)/(11-6) = -1/3
RP: slope = ((-2)-2)/(11-(-4)) = -1/3
PS: slope = (-3-2)/(2-(-4)) = -1/2
Now we can check if opposite sides are parallel and have equal length.
ST is not parallel to PQ since their slopes are not equal.
TU is parallel to RV since their slopes are both -3/2.
UV is parallel to PS since their slopes are both 2/17.
VS is not parallel to QR since their slopes are not equal.
Therefore, based on the given points, the figure is not a parallelogram, since opposite sides are not parallel or do not have equal length.