SOLUTION: 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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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(52832)   (Show Source): You can put this solution on YOUR website!
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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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