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Question 800994: A triangle has three vertices: A(3,5), B(7,1), and C(1,-1)
a)Find the equation of the perpendicular bisectors of: AB, BC, and AC
b)Find the coordinates of X, the point of intersection of the perpendicular bisector of AB and the perpendicular bisector of BC
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A triangle has three vertices: A(3,5), B(7,1), and C(1,-1)
a)Find the equation of the perpendicular bisectors of: AB, BC, and AC
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Find the line thru A & B
Slope = diffy/diffx = -4/4 = -1
Slope m of lines perpendicular is the neg inverse, m = 1
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Find the midpoint: get the average of x & y
x: (3+7)/2 = 5
y: (5+1)/2 = 3
Midpoint (5,3)
Now get the eqn of the line m = 1 thru (5,3)
Use y = mx + b and the point to find b, the y-intercept
3 = 1*5 + b
b = -2
--> eqn is y = x - 2
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Do the same for AC and BC
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b)Find the coordinates of X, the point of intersection of the perpendicular bisector of AB and the perpendicular bisector of BC
When you have the 2 eqns, solve for the point of intersection.
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