Question

HELP MARKING BRAINLIEST EXTRA POINTS !!

Answer 1

Answer:

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

Step-by-step explanation:

Given,

$A=(0,0)\\B=(1,1)\\C=(4,-2)\\D=(3,-3)$

Now,

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

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

$Perimeter=2*(AB+AD)=2*(BC+CD)\\=2*(\sqrt{2}+3\sqrt{2})=8\sqrt{2} \,\,Unit$

$Area=AB*AD=BC*CD=\sqrt{2} *3\sqrt{2}=6\,\,sq.unit$

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