Sammy is classifying quadrilateral EFGH. How can she use coordinate geometry to determine whether EFGH is a rhombus? E(2, 5), F(1, 3), G(2, 1), H(3, 3)

Sammy can use the distance formula to show that the opposite sides have equal slopes.
Sammy can use the distance formula to show that all sides are equal.
Sammy can use the slope formula to show that the opposite sides have equal slopes. Sammy can use the slope formula to show that all sides are equal.

Choice B) Sammy can use the distance formula to show that all sides are equal.

This is because, by definition, a rhombus is any four sided figure with all sides the same length. Think of a square, but we could tilt the angles and not have them all 90 degrees. So a square is a special type of rhombus.

Side note: Once Sammy has proven the figure is a rhombus, then she also has automatically proven it to be a parallelogram. Any rhombus is a parallelogram, but not the other way around.