Question

What is the most precise name for a quadrilateral with the following vertices:

Answer 1

Therefore it is a parallelogram.

Step-by-step explanation:

Given the vertices of the quadrilateral are  A(2,3) , B(7,2), C(6,-1) and D(1,0)

The length of AB is $=\sqrt{(2-7)^2+(3-2)^2}$   $=\sqrt{26}$ units

The length of BC is $=\sqrt{(7-6)^2+(2+1)^2}$  $=\sqrt{10}$ units

The length of CD is $=\sqrt{(6-1)^2+(-1-0)^2}$ $=\sqrt{26}$ units

The length of DA is  $=\sqrt{(1-2)^2+(0-3)^2}$ $=\sqrt{10}$ units

The length of AC is $=\sqrt{(2-6)^2+(3+1)^2}$ $=4\sqrt{2}$ units

The length of BD is $=\sqrt{(7-1)^2+(2-0)^2}$ = $2\sqrt{10}$ units

Here length of AB = length of CD ,

length of BC= length of DA and

length of AC ≠ length of BD

In this quadrilateral, the opposite sides are equal but the diagonals are not equal

Therefore it is a parallelogram.