Quadrilateral ABCD has coordinates A (3,1) B (4,4) C (7,5) D (6,2). Quadrilateral ABCD is a ?

The Quadrilateral ABCD with coordinates (3, 1), (4, 4), (7, 5), (6, 2) is a rhombus because its length and width are both square root of 10 units and adjacent sides are not perpendicular. This can be seen by plotting the points you can either plot it or by using programs.

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deepakrai138 deepakrai138 · Answer 2 · 2022-01-08T05:51:14+01:00

Quadrilateral ABCD is a Square.

Given,

Coordinates of quadrilateral are A(3,1), B(4,4), C(7,5), and D(6,2).

We know that, the distance formula to calculate the distance between two points [tex]( x_{1} , y_{1} )[/tex] , and[tex]( x_{2} , y_{2} )[/tex] is given as,

[tex]D =\sqrt{(x_{2} -x_{1})^2+(y_{2}-y_{1} )^2 }[/tex]

Using distance formulae, the length of AB is,

[tex]\rm AB=\sqrt{(4-3)^2+(4-1^2)}[/tex]

[tex]\rm AB=\sqrt{10}[/tex]

Similarly the length of BC will be,

[tex]\rm BC=\sqrt{10}[/tex]

[tex]\rm CD=\sqrt{10}[/tex]

And, [tex]\rm AD=\sqrt{10}[/tex]

Since all the four sides of quadrilateral ABCD are equal.

So the quadrilateral ABCD is a square.

For more details on Quadrilaterals follow the link:

https://brainly.com/question/25240753