Question

Decide whether quadrilateral ABCD with vertices 4(3,1), B(-1,-1) C(1,3), and D(5.5) is a rectangle, rhombus,square, or parallelogram.

Answer 1

Answer: rhombus

Explanation:

By inspection, we can tell that there are no right angles, so we can determine it is not a square or a rectangle.

From the options, it is implied that it is a parallelogram, so to determine if it is a rhombus, we can determine if there is a pair of consecutive congruent sides.

By the distance formula,

`AB=\sqrt{(-1-3)^(2)+(-1-1)^(2)}=√(16+4)=2√(5)\\BC=\sqrt{(-1-1)^(2)+(-1-3)^(2)}=√(4+16)=2√(5)`

As AB=BC, there is indeed a pair of consecutive congruent sides, and thus the most specific classification is a rhombus