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HELP MARKING BRAINLIEST EXTRA POINTS !!
explain how you would find the perimeter and area of the quadrilateral shown on the coordinate grid what does the slope of the segments that are what sides of the figure have to do with classifying the quadrilateral. ​

HELP MARKING BRAINLIEST EXTRA POINTS explain how you would find the perimeter and area of the quadrilateral shown on the coordinate grid what does the slope of class=

Respuesta :

Novachrono12

Answer:

  • The quadrilateral is a rectangle
  • [tex]Perimeter=8\sqrt{2} \,\,Unit[/tex]
  • [tex]Area=6\,\,sq.unit[/tex]

Step-by-step explanation:

Given,

[tex]A=(0,0)\\B=(1,1)\\C=(4,-2)\\D=(3,-3)[/tex]

Now,

[tex]Slope\,\,for\,\,AB=\frac{1-0}{1-0} =1\\\\Slope\,\,for\,\,CD=\frac{-3+2}{3-4} =1\\\\Slope\,\,for\,\,AD=\frac{-3-0}{3-0} =-1\\\\Slope\,\,for\,\,BC=\frac{-2-1}{4-1} =-1\\\\So,AB||CD\,\,and\,\,AD||BC[/tex]

[tex]AB=\sqrt{(1-0)^2+(1-0)^2}=\sqrt{2}\\BC=\sqrt{(4-1)^2+(-2-1)^2}=3\sqrt{2}\\CD=\sqrt{(3-4)^2+(-3+2)^2}=\sqrt{2}\\AD=\sqrt{(3-0)^2+(-3-0)^2}=3\sqrt{2}\\\\So,\,\,AB=CD,AD=BC\\The\,\,quadrilateral\,\,is\,\,a\,\,rectangle[/tex]

[tex]Perimeter=2*(AB+AD)=2*(BC+CD)\\=2*(\sqrt{2}+3\sqrt{2})=8\sqrt{2} \,\,Unit[/tex]

[tex]Area=AB*AD=BC*CD=\sqrt{2} *3\sqrt{2}=6\,\,sq.unit[/tex]

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