Question

show that (-3,2) , (-5,-5) , (2,-3) and (4,4) are the vertices of a rhombus.

Answer 1

hey there given 4 vertices ,
 A(-3,2),B(-5,-5) C(2,-3) and D( 4,4)
now 
using distance formula 
distance between AB = √(-5+3)² +(-5-2)² = √4 + 49 =√53
distance between BC = √(2+5)²+(-3+5)² =√49+4 =√53 
distance between CD = √(4-2)²+(4+3)² = √4 + 49 = √53
and also 
distance between AD =√(4+3)²+(4-2)² =√49+4= √53

all sides are equal 
now check for the diagonals 
AC = √(2+3)²+(-3-2)²= √25+25 = √50
now Diagonal BD =√(4+5)²+(4+5)² =√81+81 = √162


All sides are equal but diagonals arent equal, hence, it is a rhombus.

hope it helps..

Answer 2

plzz click on thanks for the answer and I hope it will be helpful for you