Question 374261: Triangle pqr has the given vertice classify the triangle by its sides. then determine if it is a right triangle
p(2,0) q (6,6) and r (12,2)
Answer by Jk22(389)   (Show Source):
You can put this solution on YOUR website! 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.
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