To determine the coordinates of the fourth vertex of the rectangle, we use the property that opposite sides of a rectangle are parallel and equal in length.

Steps:

1. Identify the given vertices:

   • $A(-6, 3)$
   • $B(-6, 5)$
   • $C(2, 3)$

2. Note that:

   • $AB$ is vertical (same $x$-coordinate, $y$-values differ).
   • $AC$ is horizontal (same $y$-coordinate, $x$-values differ).
   • The fourth vertex $D$ must be opposite $B$, completing the rectangle.

3. Since $D$ and $B$ are vertically aligned:

   • The $x$-coordinate of $D$ must be the same as the $x$-coordinate of $C$, which is $2$.

4. Since $D$ and $C$ are horizontally aligned:

   • The $y$-coordinate of $D$ must be the same as the $y$-coordinate of $B$, which is $5$.

Final Answer:

The coordinates of the fourth vertex are: $D(2, 5)$

Would you like a diagram or further explanation of this process?

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Related Questions:

1. How do we calculate the area of the rectangle given these vertices?
2. How do you verify if four points form a rectangle using slopes?
3. What are the lengths of the sides of this rectangle?
4. How would this problem change if one vertex had non-integer coordinates?
5. Can the midpoint formula be used to solve similar geometry problems?

Tip: Always double-check if opposite sides are parallel when working with rectangles on a coordinate plane!