Question

Determine whether parallelogram JKLM with vertices J(-7, -2), K(-4, 3), L(6, -3) and M(3, -8) is a rhombus, square, rectangle or all three.

Answer 1

To determine if parallelogram JKLM is a rhombus, square, or rectangle, calculate the lengths of its sides and diagonals using the distance formula and compare them.

Step-by-step explanation:

The given parallelogram JKLM has vertices J (-7, -2), K (-4, 3), L (6, -3), and M (3, -8). To determine whether it is a rhombus, square, or rectangle, we need to examine its properties.

1. Rhombus: A parallelogram is a rhombus if all its sides are congruent. Calculate the lengths of all four sides using the distance formula:

If the lengths of all four sides are equal, then the parallelogram is a rhombus.

2. Rectangle: A parallelogram is a rectangle if its diagonals are congruent. Calculate the lengths of its diagonals using the distance formula:

If the lengths of its diagonals are equal, then the parallelogram is a rectangle.

3. Square: A parallelogram is a square if it is both a rhombus and a rectangle.