posted by melissa .
the vertices of triangle ABC are A(1,7)B(9,3)C(3,1)
a.prove that the triangle is a right triangle
b.which angle is the right angle?
c.which side is the hypotnuse?
d.what are the coordinatesof the midpoint of the hypotnuse?
e.what is the equation of the median from the vertex of the right angle to the hypotnuse?
f.what is the equation of the altitude from the vertex of the right angle to the hypotnuse?
g.Is the triangle an isoceles right triangle?justify your answer using parts e and f
a. Compute the distances AB, AC and BC and show that the square of the largest number equals the squares of the two others. Most of the other questions will be obvious after you have done that. The hypotenuse will be the longest side.
The length of AB is sqrt[(9-1)^2 + (3-7)^2] = sqrt(64 + 16) = sqrt 80
The length of BC is sqrt[6^2 + 2^2] = sqrt 40.
The length of AC is sqrt[2^2 + 6^2] = sqrt 40
The triangle is a right triangle and the longest side is AB. The right angle will be opposite that side, at C.
Obviously the two short legs are equal in length. That tells you the answer to g.