Question

Decide whether parallelogram JKLM is a rectangle, a rhombus, or a square. Give all names that apply.

J(-2,7), K(7, 2), L(-2,-3). M-11,2)
rectangle
rhombus
square

Explain your reasoning.
The diagonals are neither perpendicular nor congruent.
The diagonals are perpendicular but not congruent.
The diagonals are congruent, but not perpendicular.
The diagonals are congruent and perpendicular.

Answer 1

rhombus

(b) The diagonals are perpendicular but not congruent.

Explanation:

You want to know what sort of figure the parallelogram JKLM is, given the vertices J(-2,7), K(7, 2), L(-2,-3), M(-11,2).

Observation

The x-values of points J and L on diagonal JL are the same, so that diagonal is a vertical line. Its length is 7 -(-3) = 10.

The y-values of points K and M on diagonal KM are the same, so that diagonal is a horizontal line. Its length is 7 -(-11) = 18.

The diagonals are perpendicular and not congruent, so the parallelogram is a rhombus.