Answers

  • Brainly User
2016-05-03T11:34:57+08:00
Let:
Point 1 (x₁, y₁) = (6, 2)
Point 2 (x₂, y₂) = (2, -3)
Point on the y-axis (x₃, y₃) = (0, y₃)
Note: The value of x on any point on y-axis is 0 (zero).  Therefore, x₃ = 0

Since we are looking for a point equidistant to (6,2) and (2, -3), the distant equation is:
  
     (x₃ - x₁)² + (y₃ - y₁)² = (x₃ - x₂)² + (y₃ - y₂)²

Substitute the values given:
  
     (0 - 6)² + (y₃ - 2)² = (0 - 2)² + (y₃ -  -3)²
 
     36 + (y₃)² -4y₃ + 4 = 4 + (y₃)² + 6y₃ + 9
  
     (y₃)² - 4y₃ + 40 = (y₃)² + 6y₃ + 13
 
     (y₃)² - (y₃)² - 4y₃ - 6y₃ = 13 - 40
 
     -10y₃ = -27
 
     -10y₃/-10 = -27/-10
  
      y₃ = 27/10

Therefore, the point (x₃, y₃) equidistant to the given points (6, 2) and                (2, -3) is (0,  \frac{27}{10} ).

ANSWER: (0,  \frac{27}{10} )







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