Meteorologists are planning the location of a new weather station. To optimize the radar coverage, the station must be equidistant from three cities, which are located on a coordinate plane at A(−3,1), B(5,1), and C(1,−7). What are the coordinates of the location where the station should be built?
(3, −3)
(1, −2)
(1, 1)
(−1, −3)
Answers
Given : Meteorologists are planning the location of a new weather station. , the station must be equidistant from three cities, which are located on a coordinate plane at A(−3,1), B(5,1), and C(1,−7).
To find : What are the coordinates of the location where the station should be built?
Solution:
station must be equidistant from three cities, which are located on a coordinate plane at A(−3,1), B(5,1), and C(1,−7)
Let say point is (x , y)
Then (x + 3)² + (y - 1)² = (x - 5)² + (y - 1)² = (x - 1)² + (y + 7)²
(x + 3)² + (y - 1)² = (x - 5)² + (y - 1)²
=> (x + 3)² = (x - 5)²
=> 6x + 9 = -10x + 25
=> 16x = 16
=> x = 1
(x + 3)² + (y - 1)² = (x - 1)² + (y + 7)²
using x = 1
=> 16 + y² -2y + 1 = 0 + y² + 14y + 49
=> 16y = -32
=> y = -2
(1 , - 2) are the coordinates of the location where the station should be built
Distance from each station = 5
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