Question

show that A(-3,2),B (-5,-5) c (2,-3) and D (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

Answer:

yes it is a RHOMBUS

Step-by-step explanation:

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.