SOLUTION: Please help me with this problem Use coordinate geometry to prove that quadrilateral PART with vertices P(-2,1), A(1,4), R(4,1) and T(1,-2) is a square

Please help me with this problem 
Use coordinate geometry to prove that quadrilateral PART 
with vertices P(-2,1), A(1,4), R(4,1) and T(1,-2) is a square.




Let's find the slopes of all 4 sides:


mPA =  =  =  = 

mAR =  =  = 

mRT =  =  =  = 

mTP =  =  =  = 

We need only to show that PART is a parallogram with one right angle, and
that two adjacent sides are equal in length.

PA II RT because both have the same slope 1

AR II TP because both have the same slope -1

This shows that PART is a parallelogram.

PA ^ AR because their slopes are 1 and -1, 
which are negative reciprocals of each other.  (Or rather, the product
of 1 and -1 is -1).

Now we have shown that PART is a rectangle.

Finally we show that PA = AR

DPA =  =  = =  =  = 

DAR =  =  =  =  = 

So now we have shown that PART is a square.

Edwin