Posted by **melissa** on Friday, February 20, 2009 at 11:52am.

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

- geometry -
**drwls**, Friday, February 20, 2009 at 12:03pm
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.

## Answer This Question

## Related Questions

- Math(Geometry) - In the diagram below(no diagram but details will be provided), ...
- Geometry - Write an indirect proof that an obtuse triangle does not have a right...
- Math Geometry - A triangle has vertices P(a,b), Q(c,d), and R(e,f). You are ...
- geometry - If given an a cos, sin, or tan of an angle of a right triangle, what ...
- Geometry - Please answer at least one . PLEASE 1. Triangle XYZ has a right ...
- Math-CHECK PLEASE - Which of the statements is ALWAYS TRUE? A-A right triangle ...
- math - Triangle $ABC$ is a right triangle with right angle at $A$. Suppose $\...
- geometry - Triangle ABC is a right triangle such that m angle B= 90 degrees. If ...
- geometry - TWO COLUMN TRIANGLE PROOF Given: line AB is parallel to line DE, and ...
- geometry - The medial triangle of a triangle ABC is the triangle whose vertices...

More Related Questions