Question

Determine whether the quadrilateral is a parallelogramK(2,6) L(6,12) M(13,13) N(9,8) (Use slope formula)

Answer 1

To determine if the quadrilateral is a parallelogram we can use the formula to find the distance between points, and see if their opposite sides are congruent.

The formula to calculate the distance between points is:

`\begin{gathered} d=\sqrt[]{(x_{2_{}}-x_1)^2+(y_2-y_1)^2} \\ KL=\sqrt[]{(6-2)^2+(12-6)^2} \\ KL=\sqrt[]{(4)^2+(6)^2}=\sqrt[]{52}=2\sqrt[]{13} \\ MN=\sqrt[]{(9-13)^2+(8-13)^2} \\ MN=\sqrt[]{(-4)^2+(-5)^2}=\sqrt[]{41} \end{gathered}`

Because the sides KL and MN are not congruent so it's not a parallelogram