Question

Find relation between $x$ and $y$ such that the point $(x,y)$ is equidistance them the point $(7,1)$ and $(3,5)$ .

Answer 1

• Let P(x, y) be equidistant from the points A(7, 1) and B(3, 5).
  
• Given, AP = BP
  
• AP² = BP²
  
• By distance formula,
  
• (x - 7)² + (y - 1)² = (x - 3)² + (y - 5)²
  
• x² + 49 - 14x + y² + 1 - 2y = x² + 9 - 6x + y² + 25 - 10y
  
• -7x + 25 - y = -3x + 17 - 5y
  
• -4x + 8 + 4y = 0
  
• x - y = 2