Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram,
determine whether it is also a rhombus.
-A(-2, 4), B(1, 7), C( 3, -1), D(6, 2)
A)No, it is not a parallelogram (nor is it a rhombus).
B)Yes, it is a parallelogram but it is not also a rhombus.
C)Yes, it is a parallelogram and it is also a rhombus.

Question

Quizplus · Accepted Answer

To determine if the quadrilateral is a parallelogram, we need to check if opposite sides are parallel (have the same slope). The slope of AB = (7-4)/(1+2) = 3/3 = 1, the slope of BC = (-1-7)/(3-1) = -8/2 = -4, the slope of CD = (2+1)/(6-3) = 3/3 = 1, and the slope of DA = (2-4)/(6+2) = -2/8 = -1/4. Since AB and CD have the same slope, and BC and DA have different slopes, AB is parallel to CD, indicating a parallelogram. To check if it's a rhombus, we need to see if all sides are of equal length. Calculating the distances (using the distance formula) between the points would show that the lengths of AB and BC (for example) are not equal, thus it's not a rhombus.

Use Slope to Determine Whether the Quadrilateral with the Given