Show that A(-3,-1), B(-4,-1), C(3,3) andD (4,3) are the vertices of a rhombus (R S Aggarwal pg no 668 - Maths - Coordinate Geometry

Question

Show that A(-3,-1), B(-4,-1), C(3,3) andD (4,3) are the vertices
of a rhombus (R S Aggarwal pg no 668 Q no 13)

Tushar Kohli · Accepted Answer

Let A(-3, -1), B(-4, -1),
C(3, 3) and D (4, 3)
be the vertices of rhombus ABCD

We know that, diagonals
of rhombus bisect each other

âˆ´ 
Coordinate of mid point of diagonal BD = Coordinate of mid point of
diagonal AC

Coordinate of mid point of diagonal BD = [(-4+4)/2, (-1 + 3)/2] =
(0, 1)

Coordinate of mid point of diagonal AC = [(-3 + 3)/2, (-1 + 3)/2] =
(0, 1)

Since the coordinates are equal, therefore A(-3, -1), B(-4,
-1),
C(3, 3) and D (4, 3)
are the vertices of rhombus

Show that A(-3,-1), B(-4,-1), C(3,3) andD (4,3) are the vertices of a rhombus.(R.S Aggarwal pg no. 668 Q no 13)