SOLUTION: 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 interse
Algebra.Com
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
-----
Find the line thru A & B
Slope = diffy/diffx = -4/4 = -1
Slope m of lines perpendicular is the neg inverse, m = 1
---
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
==========================
Do the same for AC and BC
=======================================
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.
RELATED QUESTIONS
Given Triangle ABC with A(2, 1), B(4, 9) and C(16,1).
a. Find the midpoints of AB, BC,... (answered by mananth)
Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6),
(a)Write the equation of... (answered by D'Leeter,Edwin McCravy)
__
Find the length of AB if AC has... (answered by CubeyThePenguin)
the points a(1,2),b(2,3) and c(3,1) are the vertices of a triangle. find [ab],[bc] and... (answered by Alan3354)
Given triangle ABC with vertices A(−3, 0), B(0, 6), and C(4, 6).
Find the equations of (answered by Alan3354,ikleyn)
Two vertices of a triangle are A(3,6) and B(7,12).
a) Find the equation of line AB.
b) (answered by MathLover1,MathTherapy)
Acute isosceles triangle ABC has vertices A(-2,-1), B(3,13), with point C on the line... (answered by greenestamps)
On the banks of a river,surveyors marked locations A,B, and C. The measure of (answered by JBarnum)
Points A, B and C are the three vertices of an isosceles triangle in which AC=BC. The... (answered by amarjeeth123,greenestamps)