Final answer:
The desired slopes and lengths of quadrilateral JKLM can be calculated using specific formulas. Based on these values, the quadrilateral can be described as a parallelogram.
Step-by-step explanation:
The slopes can be calculated using the formula m = (Y2 - Y1)/(X2 - X1).
Let's find the slopes first:
slope of JK = (0 - 4)/(3 - (-3))
= -4/6
= -2/3
slope of KL = (3 - 0)/(5 - 3)
= 3/2
slope of LM = (7 - 3)/(-1 - 5)
= 4/-6
= -2/3
slope of MJ = (4 - 7)/(-3 - (-1))
= -3/-2
= 3/2
Now, let's find the lengths:
length of JK = sqrt((3 - (-3))^2 + (0 - 4)^2)
= sqrt(36 + 16)
= sqrt(52)
= 2sqrt(13)
length of KL = sqrt((5 - 3)^2 + (3 - 0)^2)
= sqrt(4 + 9)
= sqrt(13)
length of LM = sqrt((-1 - 5)^2 + (7 - 3)^2)
= sqrt(36 + 16)
= sqrt(52)
= 2sqrt(13)
length of MJ = sqrt((-3 - (-1))^2 + (4 - 7)^2)
= sqrt(4 + 9)
= sqrt(13)
Based on the slopes and lengths, the quadrilateral JKLM can be described as a
parallelogram