SOLUTION: the points A(1,5),B(4,-1),C(-2,-4) forms a triangle ABC.Prove that the triangle is right angled and find the area.....plezz help me..........

Algebra ->  Triangles -> SOLUTION: the points A(1,5),B(4,-1),C(-2,-4) forms a triangle ABC.Prove that the triangle is right angled and find the area.....plezz help me..........       Log On


   

Question 632305: the points A(1,5),B(4,-1),C(-2,-4) forms a triangle ABC.Prove that the triangle is right angled and find the area.....plezz help me..........



Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
a = distance between B and C = sqrt%28%28-4-%28-1%29%29%5E2+%2B+%28-2-4%29%5E2%29+=+sqrt%2845%29+
b = distance between A and C = sqrt%28%28-4-5%29%5E2+%2B+%28-2-1%29%5E2%29+=+sqrt%2890%29
c = distance between A and B = sqrt%28%28-1-5%29%5E2+%2B+%284-1%29%5E2%29+=+sqrt%2845%29
Therefore a%5E2+%2B+c%5E2+=+b%5E2 because %28sqrt%2845%29%29%5E2+%2B+%28sqrt%2845%29%29%5E2+=+%28sqrt%2890%29%29%5E2.
The sides satisfy the Pythagorean Theorem, therefore triangle ABC is a right triangle with angle B as a right angle.
the area is equal to
A+=+%28base%29%28height%29%2F2
A+=+%28sqrt%2845%29%29%28sqrt%2845%29%29%2F2
highlight%28A+=+22.5%29 square units