Prove that: `(4,-1) , (6,0) , (7,2)` and `(5,1)`  are the vertices o a rhombus. Is it a square?

Explanation

We have to proof `(4,-1) , (6,0) , (7,2)` and `(5,1)`are the vertices of a rhombus.

Let the points be `A=(4,-1)`, `B=(6,0)`, `C=(7,2)` and `D=(5,1)` respectively.

Then,Coordinates of the mid-point of AC are`((4+7)/2,(-1+2)/2)=(11/2,1/2)`

Coordinates of the mid-point of BD are`((6+5)/2,(0+1)/2)=(11/2,1/2)`

Thus, AC and BD have the same mid-point.
So, ABCD is a parallelogram.
Now, `AB=sqrt((6−4)^2+(0+1)^2)=sqrt(5),BC=sqrt((7−6)^2+(2-0)^2)=sqrt(5),`

`\Rightarrow AB=BC`

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