Question 8569
A(0,4), B(1,2), and C(4,6). 
 mAB(slope of AB) = (2-4)/1 =-2,

 mBC(slope of BC) = (6-2)/(4-1) = 4/3,

 mAC(slope of AC) = (6-4)/(4-0) = 1/2,

 Now, we see that mAB*MAC = -1, so AB  & AC are perpendicular
 and so A is a right angle & ABC is a right triangle.

 Note useing slope is the simplest way to solve this kind of questions.

 kenny