Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.

A(3, − 9), B(10, 1), C(4, 10), D(−9, 3); Distance and Slope Formulas

1 answer

so parallelograms must have opposite sides congruent, in this case AB and CD, and BC and AD.

Using the distance formula:
AB=sqrt((10-3)^2+(1-(-9))^2)
sqrt(7^2+10^2)
sqrt(149)

CD=sqrt((-9-4)^2+(3-10)^2)
sqrt(-13^2+-7^2)
sqrt(169+49)
sqrt(218)

Since AB is not equal to CD, this figure cannot be a parallelogram