In the endgame of chess, the position of King and Rook vs King is a fundamental checkmating scenario. The player with the rook can force the opponent's king to the edge of the board, using the rook to control key squares while the king supports the rook's movements. To achieve checkmate, the rook should be placed one rank or file away from the opposing king, while the player's king moves in to help. This coordinated effort will eventually corner the opponent's king, leading to a checkmate where the rook delivers the final blow.