Question

The vertices of a quadrilateral are at the coordinates (1, 3), (2, 5), (5, 1), and (6, 3). Which of the following properties describe the quadrilateral? Select all that apply.

a. all sides are congruent

b.the diagonals are congruent

c.both pair of opposite sides are parallel

d.both pairs of opposite sides are congruent

e.exactly one pair of sides are parallel

Answer 1

The properties that describe the quadrilateral are-

(b) the diagonals are congruent

(c) both pair of opposite sides are parallel

(d) both pairs of opposite sides are congruent

Explanation:-

Let, A=(1,3); B=(2,5); C=(5,1); D=(6,3)

So side AB= √{(1-2)2 + (3-5)2}=√5 unit

Similarly, BC= 5 unit

CD= √5 unit

DA= 5 unit

So opposite sites are congruent and they must be parallel.

Now diagonal AC= √{(1-5)2+(3-1)2} = √20 unit

and BD=√{(2-6)2+(5-3)2} = √20 unit

Thus the diagonals are congruent.