If point $$(x, y)$$ is equidistant from the points $$(7, 1)$$ and $$(3, 5)$$, then which one of the following options is correct?

Question

Accepted Answer

1. **Apply the distance formula**:  
   Since the point $$(x, y)$$ is equidistant from both points:  
   $$
   \sqrt{(x - 7)^2 + (y - 1)^2} = \sqrt{(x - 3)^2 + (y - 5)^2}.
   $$

2. **Square both sides to eliminate the square root**:  
   $$
   (x - 7)^2 + (y - 1)^2 = (x - 3)^2 + (y - 5)^2.
   $$

3. **Expand both sides**:  
   Left-hand side:  
   $$
   x^2 - 14x + 49 + y^2 - 2y + 1.
   $$  
   Right-hand side:  
   $$
   x^2 - 6x + 9 + y^2 - 10y + 25.
   $$

4. **Simplify by canceling common terms**:  
   $$
   -14x + 49 - 2y + 1 = -6x + 9 - 10y + 25.
   $$  
   Combine like terms:  
   $$
   -14x + 49 - (-6x) = -10y + 25 - (-2y).
   $$  
   $$
   -8x + 8y = -16.
   $$

5. **Divide through by $$-8$$**:  
   $$
   x - y = 2.
   $$

Thus, the equation is **$$x - y = 2$$**, and the correct answer is **(a)**.

Answer

Answer

Answer