Question

Prove thst A(-1,-2),B(1,0)C(-1,2) D(-3,0)are the vertices of a square

Answer 1

Answer:

Given points are

A(−2,−1),B(1,0),C(4,3) and D(1,2)

A quadrilateral is a parallelogram if the opposite sides are equal.

∴AB

2

=(−2−1)

2

+(−1−0)

2

=9+1

=10

BC

2

=(4−1)

2

+(3−0)

2

=9+9

=18

CD

2

=(1−4)

2

+(2−3)

2

9+1

=10

AD

2

=(−2−1)

2

+(−1−2)

2

=9+9

=18

∴AB=CD=

10

and BC=AD=

18

∴ The opposite sides of the quadrilateral ABCD are equal, the four points from a parallelogram.