(Q33)Name the type of quadrilateral formed, if any,by the following points, and give reasons for your answer
(i)(-1,-2),(1,0),(-1,2),(-3,0).

Answer:

Let A(-1,-2) B(1,0) C(-1,2) D(-3,0) be the given points.Distance formula

=√((x2 - x1)2 + (y2 - y1)2)

AB=√((+)2 + (+)2)

=√

=√2

BC=√((--)2 + (-)2)

=√

=√2

CD=√((-+)2 + (-)2)

=√

=√2

AD=√((-+)2 + (+)2)

=√

=√2

AC=√((-+)2 + (+)2)

=√

=units

BD=√((--)2 + (-)2)

=√

=units

In ABCD AB=BC=CD=AD - four sides are equal.

AC=BD diagonals are equal.

Hence the given points form a square.