SOLUTION: Three friends are planning to visit each other. To optimize travel time, they want the meeting place to be equidistant from the three different cities they live in. The cities are

Algebra ->  Graphs -> SOLUTION: Three friends are planning to visit each other. To optimize travel time, they want the meeting place to be equidistant from the three different cities they live in. The cities are       Log On


   

Question 972365: Three friends are planning to visit each other. To optimize travel time, they want the meeting place to be equidistant from the three different cities they live in. The cities are located at A(-16, -1), B(1, 6), and C(1, -18). What are the coordinates where the meeting should take place?
help me please thank you show work please.:)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have 3 lines here:
AB
BC
CA
--------
You need to find the equations for the
perpendicular bisectors of each of these
lines
--------
AB
+%28+-16+%2B+1+%29+%2F+2+=+-15%2F2+
+x%5BAB%5D+=+-15%2F2+
+%28+-1+%2B+6+%29+%2F+2+=+5%2F2+
+y%5BAB%5D+=+5%2F2+
----------------
So the center of the line AB is
at ( -15/2 , 5/2 )
-----------------
What's he slope of AB?
+m+=+%28+-1+-+6+%29+%2F+%28+-16+-+1+%29+
+m+=+7%2F17+
The slope perpendicular to this is:
+m+=+-17%2F7+
----------------
Now use point-slope formula:
+%28+y+-+6+%29+%2F+%28+x+-+1+%29+=+-17%2F7+
+y+-+6+=+%28-17%2F7%29%2A%28+x+-+1+%29+
+7y+-+42+=+-17x+%2B+17+
+7y+=+-17x+%2B+59+
+y+=+%28-17%2F7%29%2Ax+%2B+59%2F7+
--------------------------
This is the equation of the perpendicular bisector of AB
( if my math is right )
---------------------
Now do the exact same steps for BC and CA
The 3 lines you get should meet at the same point.
( the simultaneous solution )
This is the point equidistant from the 3 given points
Hope this helps