SOLUTION: Given triangle ABC with vertices A(0,4) ,B(-6,0) and C(2,0) , where l,m and n are the perpendicular lines bisecting AB,AC and BC, respectively. Obtain the equation of l,m and n.

Algebra ->  Rational-functions -> SOLUTION: Given triangle ABC with vertices A(0,4) ,B(-6,0) and C(2,0) , where l,m and n are the perpendicular lines bisecting AB,AC and BC, respectively. Obtain the equation of l,m and n.      Log On


   

Question 1062291: Given triangle ABC with vertices A(0,4) ,B(-6,0) and C(2,0) , where l,m and n are the perpendicular lines bisecting AB,AC and BC, respectively. Obtain the equation of l,m and n.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
AB
--------
A(0.4)
B(-6,0)
midpoint:
+M%5Bx%5D+=+%28+0+%2B%28-6%29+%29+%2F+2+=+-3+
+M%5By%5D+=+%28+4+%2B+0+%29+%2F+2+=+2+
( -3,2 )
----------
slope:
+%28+4+-+0+%29+%2F+%28+0+-%28-6%29+%29+=+4%2F6+
+4%2F6+=+2%2F3+
perpendicular slope:
+-3%2F2+
========================
AC
-------
A(0,4)
C(2,0)
midpoint:
+M%5Bx%5D+=+%28+0+%2B+2+%29+%2F+2+=+1+
+M%5By%5D+=+%28+4+%2B+0+%29+%2F+2+=+2+
( 1,2 )
---------
slope:
+%28+4+-+0+%29+%2F+%28+0+-+2+%29+=+-2+
perpendicular slope:
+1%2F2+
=========================
BC
-------
B(-6.0)
C(2,0)
midpoint:
+M%5Bx%5D+=+%28+-6+%2B+2+%29+%2F+2+
+M%5Bx%5D+=+-4%2F2+
+M%5Bx%5D+=+-2+
and
+M%5By%5D+=+%28+0+%2B+0+%29+%2F+2+=+0+
( -2,0)
---------
slope:
+%28+0+-+0+%29+%2F+%28+2+-%28-6%29+%29+=+0+
perpendicular slope = vertical line
through the midpoint
+x+=+-2+
=========================
=========================
equation for L:
( -3,2 )
m = -3/2
-------------
+%28+y+-+2+%29+%2F+%28+x+-%28-3%29+%29+=+-3%2F2+
+%28+y+-+2+%29+%2F+%28+x+%2B+3+%29+=+-3%2F2+
+2%2A%28+y+-+2+%29+=+-3%2A%28+x+%2B+3+%29+
+2y+-+4+=+-3x+-+9+
+2y+=+-3x+-+5+
+y+=+%28-3%2F2%29%2Ax+-+5%2F2+
=========================
Equation for M:
( 1,2 )
m = 1/2
+%28+y+-+2+%29+%2F+%28+x+-+1+%29+=+1%2F2+
+2%2A%28+y+-+2+%29+=+x+-+1+
+2y+-+4+=+x+-+1+
+2y+=+x+%2B+3+
+y+=+%281%2F2%29%2Ax+%2B+3%2F2+
=========================
Equation for N:
( -2,0 )
m = vertical line
+x+=+-2+
==========================
Whew!
Check the math