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Quadrilateral ABCD has coordinated a(-4,3) b(-3,6) c(0,8) d(-2,5). Prove that quadrilateral ABCD is a parallelogram and explain whether quadrilateral ABCD is a rectangle or not.

Answer :

Quadrilateral ABCD has coordinate

A(-4, 3) , B(-3, 6) C(0,8) & D(-2,5)

so we will find the length of the sides

[tex]AB=\sqrt[]{(6-3)^2+(-3-(-4))}^2=\sqrt[]{9+1}=\sqrt[]{10}[/tex]

for CD

[tex]CD=\sqrt[]{(5-8)^2+(-2-0)^2}=\sqrt[]{9+4}=\sqrt[]{13}[/tex]

as we can see AB and CD is not equal to Quadrilateral is not equal.

now we compute the midpoint of the diagonals

midpoint of

[tex](x,y)=(\frac{-4-3}{2},\frac{3+6}{2})=(-\frac{7}{2},\frac{9}{2})[/tex]

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