SOLUTION: Show in two ways that the points (6,1), (2-3), and (4-5) are the vertices of a right Triangle . //help me please . Thanks :)

Algebra ->  Trigonometry-basics -> SOLUTION: Show in two ways that the points (6,1), (2-3), and (4-5) are the vertices of a right Triangle . //help me please . Thanks :)      Log On


   

Question 981367: Show in two ways that the points (6,1), (2-3), and (4-5) are the vertices of a right Triangle .
//help me please . Thanks :)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You meant (6,1), (2,-3), and (4,-5), which indeed are the vertices of a right triangle.


ONE WAY:
Show that the line connecting (6,1) and (2,-3) has a slope of 1.
Show that the line connecting (4,-5) and (2,-3) has a slope of -1.
Since the product of the slopes is %281%29%28-1%29=-1 , the lines are perpendicular,
so the triangle has a right angle at (2,-3).
The slope the line connecting A%286%2C1%29 and C%282%2C-3%29 is
%281-%28-3%29%29%2F%286-2%29+=%281%2B3%29%2F4=4%2F4=1
The slope the line connecting B%284%2C-5%29 and C%282%2C-3%29 is
%28-5-%28-3%29%29%2F%284-2%29+=%28-5%2B3%29%2F2=-2%2F2=-1

ANOTHER WAY:
Show that the lengths of the sides satisfy the Pythagorean theorem:
c%5E2=a%5E2%2Bb%5E2
c%5E2=%286-4%29%5E2%2B%281-%28-5%29%29%5E2=2%5E2%2B6%5E2=4%2B36=40
a%5E2=%282-4%29%5E2%2B%28-3-%28-5%29%29%5E2=%28-2%29%5E2%2B2%5E2=4%2B4=8
b%5E2=%286-2%29%5E2%2B%281-%28-3%29%29%5E2=4%5E2%2B4%5E2=16%2B16=32