Question 374261
p(2,0) q (6,6) and  r (12,2)
 
side length : |pq|=|(6-2,6-0)|=|(4,6)|=sqrt(16+36)=sqrt(52)
 
|pr|=|(12-2,2-0)|=|(10,2)|=sqrt(104)

|qr|=|(12-6,2-6)|=|(6,-4)|=sqrt(36+16)|=sqrt(52)
 
two sides are equal, it's an isoceles triangle.
 
 

angles : (dot product, if a.b=0 the 2 vectors are orthogonal) 
 
pq.pr=40+12<>0
 
pq.qr=4*6-6*4=0 (for verif : pr*qr=60-8<>0)
 
hence the triangle is rectangle and has a right angle in q.


{{{drawing( 300, 150, 0, 15, 0, 7.5,
  grid( 1 ),
  line(2,0,6,6),
  line(2,0,12,2),
   line(6,6,12,2),
  locate(2,1,p), locate(6,6,q),locate(12,2,r)
)}}}