Question

PLEASE HELP

What is the most specific name for quadrilateral WXYZ?
O square
O rectangle
O parallelogram
O rhombus

Answer 1

Its A, square

Explanation:

I just took the quiz. :)

Answer 2

Option (1)

Explanation:

Coordinates of the vertices of a quadrilateral WXYZ drawn in the figure are,

W(-1, 4), X(2, 2), Y(0, -1), Z(-3, 1)

Length of a segment having ends as
`(x_1, y_1)` and
`(x_2, y_2)` is represented by,

d =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Length of WX =
`√((-1-2)^2+(4-2)^2)`

=
`√(9+4)`

=
`√(13)`

Length of XY =
`√((2-0)^2+(2+1)^2)`

=
`√(13)`

Length of YZ =
`√((0+3)^2+(-1-1)^2)`

=
`√(13)`

Length of ZW =
`√((-1+3)^2+(4-1)^2)`

=
`√(13)`

Slope of side WX (
`m_1`) =
`(y_2-y_1)/(x_2-x_1)`

=
`(4-2)/(-1-2)`

=
`-(2)/(3)`

Slope of side XY (
`m_2`) =
`(2+1)/(2-0)`

=
`(3)/(2)`

By the property of perpendicular lines,

`m_1* m_2=-1`

`(-(2)/(3))((3)/(2))=-1`

therefore, WX and XY are perpendicular.

Slope of YZ (
`m_3`) =
`(-1-1)/(0+3)=-(2)/(3)`

`m_2* m_3=((3)/(2))* (-(2)/(3))=-1`

Therefore, XY ⊥ YZ

Similarly, we can prove YZ ⊥ ZW.

Therefore, quadrilateral WXYZ is a SQUARE.

Option (1) will be the answer.