Question

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

A(2,3) B(7,2) C(6,-1) D(1,0)

Answer 1

Therefore it is a parallelogram.

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
`=√((2-7)^2+(3-2)^2)`
`=√(26)` units

The length of BC is
`=√((7-6)^2+(2+1)^2)`
`=√(10)` units

The length of CD is
`=√((6-1)^2+(-1-0)^2)`
`=√(26)` units

The length of DA is
`=√((1-2)^2+(0-3)^2)`
`=√(10)` units

The length of AC is
`=√((2-6)^2+(3+1)^2)`
`=4√(2)` units

The length of BD is
`=√((7-1)^2+(2-0)^2)` =
`2√(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.