Question

Determine whether parallelogram JKLM with vertices J(-7, -2), K(0, 4), L(9, 2) and M(2, -4) is a rhombus, square, rectangle or all three.

Answer 1

@mathmate

Answer 2

First:
we are given that JKLM is a parallelogram, so lines JK and LM should be parallel, so should JM and KL.
At this point, a diagram would be helpful, at least for the nomenclature of the sides.

If the parallelogram is a rhombus, then all four sides are congruent, i.e.
JK=KL=LM=MJ
Given that it is a parallelogram, we need only check equality of adjacent sides, using the distance formula:
\(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Alternatively, if it is a rhombus, JL and KM intersect at right-angles.
This can be checked using
\(Slope(JL)*Slope(KM)=-1\)
For a rectangle, at least one of the interior angles of a parallelogram must be 90 degrees.
This again can be checked using slopes, for example:
\(Slope(KJ)*Slope(JM)=-1\)
If it is a rhombus AD a rectangle, then automatically it is a square ("all three").

Answer 3

thank you

Answer 4

You're welcome! :)
I hope you got everything you need to complete the problem.

Answer 5

yes i do thank you

Answer 6

No problem!