Show that points P(2,-2) , Q (7,3) ,R(11,-1) and S(6,-6)
are vertices of a parallelogram.

Explanation

Proof:
`P(2,-2),Q(7,3),R(11 ,-1)` and `S(6,-6)`
By distance formula.
`PQ=sqrt((7-2)^(2)+[3-(-2)]^(2))`
`:.PQ=sqrt(5^(2)+5^(2))`
`:.PQ=sqrt(5^(2)+5^(2))`
`:.PQ=sqrt(25+25)`
`:.PQ=sqrt(50)`
`:.PQ=sqrt(5xx5xx2)`
`:.PQ=5sqrt(2)` ........1
`QR =sqrt((11-7)^(2)+(-1-3)^(2))`
`:.QR=sqrt(4^(2)+(-4)^(2))`
`:.QR=sqrt(16+16)`
`:.QR=sqrt(32)`
`:.QR=sqrt(2xx2xx2xx2xx2)`
`:.QR=4sqrt(2)` ..........2
`RS=sqrt((6-11)^(2)+[-6-(-1)]^(2))`
`:.Rs=sqrt((-5)^(2)+(-5)^(2))`
`:.RS=sqrt(25+25)`
`:.RS=sqrt(50)`
`:.RS=sqrt(5xx5xx2)`
`:.RS=5sqrt(2)`...........3
`PS=sqrt((6-2)^(2)+[-6-(-2)]^(2))`
`:.PS=sqrt(4^(2)+(-4)^(2))`
`:.PS=sqrt(16+16)`
`:.PS=sqrt(32)`
`:.PS=sqrt(2xx2xx2xx2xx2)`
`:.PS=2xx2xxsqrt(2)`
`:.PS=4sqrt(2)`.............4
In `square PQRS`
`PQ=RS` .......[From 1 and 3]
`QR=PS`......[From 2 and 4]
A quadrilaterial is a parallelogram, if both the pairs of its opposite sides are congruent.
`:.square PQRS` is a parallelogram.
`P(2,-2),Q(7,3),R(11,-1)` and `S(6,-6)` are vertices of a parallelogram.