Question

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 1

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

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

for CD

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

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

`(x,y)=((-4-3)/(2),(3+6)/(2))=(-(7)/(2),(9)/(2))`