Three villages are located around the circle at (2,-1) (-3,2) and (-2,-4). A health center should be located at a point so that all three villages can reach the center in the same distance.
Find the point at which the health center can be located
Answers
Given:
Three villages are located around the circle at (2,-1) (-3,2) and (-2,-4). A health centre should be located at a point so that all three villages can reach the centre in the same distance.
To find:
Find the point at which the health centre can be located
Solution:
From given, we have,
Three villages are located around the circle at (2,-1) (-3,2) and (-2,-4).
Let A (2,-1) B (-3,2) and C (-2,-4).
The distance formula is,
d = √[ (x₂ - x₁)² + (y₂ - y₁)² ]
⇒ d² = (x₂ - x₁)² + (y₂ - y₁)²
As the distance to be the same, so, we will equate the same.
OA = OB
√[ (x - 2)² + (y + 1)² ] = √[ (x + 3)² + (y - 2)² ]
x² + 4 - 4x + y² + 1 + 2y = x² + 9 + 6x + y² + 4 - 4y
5 - 4x + 2y = 13 + 6x - 4y
5x - 3y + 4 = 0 ...... (1)
OC = OB
√[ (x + 2)² + (y + 4)² ] = √[ (x + 3)² + (y - 2)² ]
x² + 4 + 4x + y² + 16 + 8y = x² + 9 + 6x + y² + 4 - 4y
20 + 4x + 8y = 13 + 6x - 4y
2x - 12y - 7 = 0 ....... (2)
Solve equations (1) and (2)
x = -23/18 and y = -43/54
Therefore, the health center should be located at a point so that all three villages can reach the center in the same distance is (-23/18, -43/54)
Answer:
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