To find the relation between $x$ and $y$ such that the point $(x, y)$ is equidistant from the points $(3, 1)$ and $(2, 0)$, we need to use the distance formula.

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Since the point $(x, y)$ is equidistant from both $(3, 1)$ and $(2, 0)$, the distances must be equal:

$\sqrt{(x - 3)^2 + (y - 1)^2} = \sqrt{(x - 2)^2 + (y - 0)^2}$

Now, square both sides to eliminate the square roots:

$(x - 3)^2 + (y - 1)^2 = (x - 2)^2 + y^2$

Expand both sides:

$(x^2 - 6x + 9) + (y^2 - 2y + 1) = (x^2 - 4x + 4) + y^2$

Simplify the equation by canceling out the $x^2$ and $y^2$ terms on both sides:

$-6x + 9 - 2y + 1 = -4x + 4$

Now simplify further:

$-6x - 2y + 10 = -4x + 4$

Move all terms involving $x$ and $y$ to one side:

$-6x + 4x - 2y = 4 - 10$

$-2x - 2y = -6$

Divide the equation by $-2$ to simplify:

$x + y = 3$

Thus, the relation between $x$ and $y$ is:

$x + y = 3$

Would you like further details or have any questions?

Here are some related questions:

1. How can this relation be interpreted geometrically?
2. What if the points were different, say $(1, 2)$ and $(3, 4)$?
3. How does the midpoint of $(3, 1)$ and $(2, 0)$ relate to this equation?
4. Can this problem be solved using vectors?
5. How would the solution change if we had three points instead of two?

Tip: When solving geometry problems, drawing a diagram can help visualize the relations and guide you through the solution.