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.Com
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)   (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




----------------
So the center of the line AB is
at ( -15/2 , 5/2 )
-----------------
What's he slope of AB?


The slope perpendicular to this is:

----------------
Now use point-slope formula:





--------------------------
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


RELATED QUESTIONS

Two friends are 60 miles apart. They decide to ride their bicycles to meet each other.... (answered by richwmiller)
Three friends want to equally share five oranges, How many oranges are there for each of... (answered by stanbon)
Hello,distance and time are not really my strong points... Winnie and Piglet decided to... (answered by ikleyn,solver91311)
Two friends, Robbie and Megulo, live 2200 miles apart. They want to meet each other and... (answered by josgarithmetic)
Two friends, Frank and Jack, live 2000 miles apart. They want to meet each other and... (answered by addingup)
2 postmen leave at the same time from cities A and B, respectively, & travel toward the... (answered by richwmiller)
Please help with this. There are two cities, A and B, on the opposite sides of a big... (answered by richwmiller,ankor@dixie-net.com)
Two carloads of friends are driving cross-country from Connecticut to San Francisco. One... (answered by Stitch)
Hello, I am trying to imagine using three flash lights in a ball to light it up... (answered by Alan3354)