If the points A(-4, -2) , B (-3,-7) , C(3,-2) and D(2,3) are
joined serially , find the type of quadrilateral ABCD by completing
the following activity.

Explanation

`A(-4,-2),B(-3,-7),C(3,-2)` and `D(2,3)`
By distance formula,
`AB=([-3-(-4)]^(2)+[-7-(-2)]^(2))`
`=sqrt((-3+4)^(2)+(-7+2)^(2))`
`=sqrt(1^(2)+(-5)^(2))`
`=sqrt(1+25)`
`sqrt(26)`……..1
`BC=sqrt([3-(-3)]^(2)+[-2-(-7)]^(2))`
`=sqrt(6^(2)+5^(2))`
`=sqrt(36+25)`
`=sqrt(61)`...............2
`CD=sqrt((2-3)^(2)+[3-(-2)]^(2))`
`=sqrt((-1)^(2)+(5)^(2))`
`=sqrt(1+25)`
`=sqrt(26)` ........3
`AD=sqrt([2-(-4)]^(2)+[3-(-2)]^(2))`
`=sqrt(6^(2)+5^(2))`
`=sqrt(36+25)`
`=sqrt(61)`............4
`AC=sqrt([3-(-4)]^(2)+[-2-(-2)]^(2))`
`=sqrt((3+4)^(2)+(-2+2)^(2))`
`=sqrt(7^(2)+0^(2))`
`=sqrt(49)`
`=7` ......5
`Bd=sqrt([2-(-3)]^(2)+[3-(-7)]^(2))`
`=sqrt(5^(2)+10^(2))`
`=sqrt(25+100)`
`=sqrt(125)`
`=sqrt(5xx5xx5)`
`=5sqrt(5)`...........6
In `square ABCD`
`AB=CD`......[From 1 and 3]
`BC=AD` .......[From 2 and 4]
`AC!=BD`..........[From 5 and 6]
`:.squareABCD` is a parallelogram.
...........(A quadrilaterial is a parallelogram, if its opposite sides are congruent)
Points `A(-4,-2),B(-3,-7),C(3,-2)` and `D(2,3)` form a parallelogram.