Show that the points (4, 6), (-1, 5), (-2, 0), (3,
1) are the vertices of a rhombus.

|AB|=|BC|=|CD|=|DA|=√26

This shows that the points are vertices of a rhombus.

Step-by-step explanation:

Show that the points (4, 6), (-1, 5), (-2, 0), (3, 1) are the vertices of a rhombus, we simply have to show that they all have equal distances.

Let ABCD be the vertices of the rhombus (4, 6), (-1, 5), (-2, 0), (3, 1)  respectively.  That is;

A(4, 6), B(-1, 5), C(-2, 0), D(3, 1)  

We will find the distance AB, BC, CD and DA, If the distances between them are equal, then we are able to prove that it is a rhombus;

Using the distance formula;

D = √( - )² + ( - )²

Distance AB

A(4, 6), B(-1, 5)

=4        =6       =-1     =5

|AB|=√( - )² + ( - )²

         =√(5- 6)² + (-1- 4)²

           =√(-1)² + (-5)²

           =√1+ 25

           =√26

Distance BC

B(-1, 5), C(-2, 0)

=-1        =5     =-2   =0

|BC|=√( - )² + ( - )²

      =√(0 - 5)² + (-2+1)²

       =√(-5)² + (-1)²

       =√25+1

        =√26

Distance CD

C(-2, 0), D(3, 1)

=-2       =0     =3   =1

|CD|=√( - )² + ( - )²

      =√(1 - 0)² + (3+2)²

       =√(1)² + (5)²

       =√1+25

        =√26

Distance DA

D(3, 1)  A(4,6)

=3     =1     =4   =6

|DA|=√( - )² + ( - )²

      =√(6 - 1)² + (4-3)²

       =√(5)² + (1)²

       =√25+1

        =√26

|AB|=|BC|=|CD|=|DA|=√26

This shows that the points are vertices of a rhombus.

okay wait before i answer, is this for your points on a graph?

yes

step-by-step explanation: