Without using distance formula, show that points `(2," "1)` , `(4," "0)` , `(3," "3)` and `(3," "2)` are the vertices of a parallelogram.

Explanation

Let points (-2,-1),(4,0),(3,3) and (-3,2) be respectively denoted by A, B, C and D.

Now, slope of A B=`frac(0+1)(4+2)=frac16`

Slope of CD =`frac(2-3)(-3-3)=frac(-1)(-6)=frac(1)6`

Rightarrow slope of A B= slope of C D

Rightarrow A B and C D are parallel to each other

Also, slope of mathrmBC=`frac(3-0)(3-4)=frac(3)(-1)=-3`

Slope of A D=`frac(2+1)(-3+2)=frac(3)(-1)=-3`

Rightarrow slope of B C= slope of A D

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