Question

Name the type of quadrilateral formed, if any by the following points and give reason for your answer.
(-1,-2), (1,0), (-1,2), (-3,0)

Answer 1

Heya !
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Kindly refer to the attachment.

☆ Hope thishelps.

Answer 2

heya..

Using Distance Formula to find distances AB, BC, CD and DA, we get

AB=√{1-(1)}^2+{0-(-2)}^2=√(2)^2+(2)^2=√4+4=√8=2√2

BC=√{-1-1}^2+{2-0}^2=√(-2)^2+(2)^2=√4+4=√8=2√2

CD=√{-3-(-1)}^2+{0-2}^2=√(-2)^2+(-2)^2=√4+4=√8=2√2

AD=√{-3-(-1)}^2+{0-(-2)}^2=√(-2)^2+(2)^2=√4+4=√8=2√2

Therefore, all four sides of quadrilateral are equal.        … (1)

Now, we will check the length of diagonals.

AC=√{-1-(-1)}^2+{2-(-2)}^2=√(0)^2+(4)^2=√16=4

BD=√{-3-1}^2+{0-0}^2=√(4)^2+(0)^2=√16+0=4

Therefore, diagonals of quadrilateral ABCD are also equal.        … (2)

From (1) and (2), we can say that ABCD is a square.

tysm.@kundan