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.

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

Step-by-step explanation:

Sammy can use the distance formula to show that all sides are equal. A rhombus has 4 congruent sides, so finding the distance of all the sides and determining that they are all equal would make a rhombus.

Step-by-step explanation: This is the only option that makes sense.  If you think about it, a rhombus has two pairs of parallel sides and 4 congruent sides.  If you were to use the distance formula to find out that all sides are congruent, then it might mislead you into thinking it was a square.  However, if you use the slope formula to find that that opposites sides have equal slopes and are parallel.  This is something that applies to a rhombus and not a square.  Therefore, answer C. is the correct choice.