Question

name the type of Quadrilateral formed by the points(-1, ;2), (1.0) , (-1, 2), (-3, 0) and give reason for your answer​

Answer 1

let

A(-1,2)

B(1,0)

C(-1,-2)

D(-3,0)

here we find all the points are such that AB is perpendicular to BC

BC perpendicular to CD

CD perpendicular to AD

AD perpendicular to AB

and AB=2 root 2

BC =2 root 2

CD =2 root 2

AD =2 root 2

here all the sides length is equal and all sides are perpendicular to each other so the quadrilateral formed by points (-1, ;2), (1.0) , (-1,-2), (-3, 0)

is square

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Answer 2

Let A(-1,2) ; B(1,0) ; C(-1,2)  and  D(-3,0) be the vertices of the triangle

Area of triangle ABC =

X1(y2-y3) + X2(y3-y1) + X3(y1-y2)

= -1(0-2) +1(2-2) +(-1)(2-0)

= 2 + 0 -2

= 0 unit²

similarly

Area of triangle ADC =

X1(y2-y3) + X2(y3-y1) + X3(y1-y2)

= -1(0-2) + -3(2-2) + -1(2-0)

= 2 + 0 -2

= 0 unit²

Since , Ar (ΔABC) = Ar(ΔADC)

The quadilateral so formed is a square