SOLUTION: Hello, would any tutors please help me with these problems? I don't really understand how to do them. If also you can explain how you did them, I would be really thankful. Thank yo

Algebra ->  Triangles -> SOLUTION: Hello, would any tutors please help me with these problems? I don't really understand how to do them. If also you can explain how you did them, I would be really thankful. Thank yo      Log On


   

Question 602769: Hello, would any tutors please help me with these problems? I don't really understand how to do them. If also you can explain how you did them, I would be really thankful. Thank you for your time!!!
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Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
13.A
A(2,8)
B(0,8)
C(2,2)
Let O be the center of the circle circumscribing the triangle
Then d(OA)=d(OB)=d(OC) all are radii.
Let the coordinates of be (x,y)
The distance between two points (x1,y1) & (x2,y2) is given by
d=sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
O(x,y) & A(2,8)
d(OA)= sqrt%28%288-y%29%5E2%2B%282-x%29%5E2%29
=sqrt%2864-16y%2By%5E2%2B4-4x%2Bx%5E2%29
=sqrt%28x%5E2%2By%5E2-4x-16y%2B68%29
B(0,8)O(x,y)
d(OB)= sqrt%28%288-y%29%5E2%2B%280-x%29%5E2%29=sqrt%2864-16y%2By%5E2%2Bx%5E2%29
Since OA & OB are radii
They are equal
sqrt%28x%5E2%2By%5E2-4x-16y%2B68%29=sqrt%2864-16y%2By%5E2%2Bx%5E2%29
square both sides
x%5E2%2By%5E2-4x-16y%2B68=64-16y%2By%5E2%2Bx%5E2
-4x=-68+64
=-4x=-4
x=1
C(2,2) O(x,y)
D(OC)= sqrt%28%28y-2%29%5E2%2B%28x-2%29%5E2%29
=sqrt%28y%5E2-4y%2B4%2Bx%5E2-4x%2B4%29
=sqrt%28x%5E2%2By%5E2-4x-4y%2B8%29
d(OC)=d(OA)
sqrt%28x%5E2%2By%5E2-4x-4y%2B8%29=sqrt%28x%5E2%2By%5E2-4x-16y%2B68%29
square both sides
x%5E2%2By%5E2-4x-4y%2B8%29=x%5E2%2By%5E2-4x-16y%2B68
12y=60
/12
y=5
The center (1,5)
17 bisector
18 median
19 altitude

m.ananth@hotmail.ca