Question 1016825: show that the points(4,0),(2,1),(-1,-5) are the vertices of a right triangle and find its area.
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
show that the points (4,0), (2,1), (-1,-5) are the vertices of a right triangle and find its area.
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This is your triangle.
Calculate the distances between the given points (4,0), (2,1), (-1,-5).
1. Points (4,0) and (2,1). The distance a =  =  =  .
2. Points (2,1) and (-1,-5). The distance b =  =  =  =  .
3. Points (4,0) and (-1,-5). The distance c =  =  =  =  .
Now you see that  +  = 5 + 45 = 50 =  .
It is just enough to conclude that the triangle is right-angled.
Next, the area of the triangle is  =  =  =  = 7.5  .
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