https://www.chess.com/article/view/basic-checkmates-king-and-rook-mate
Rook and King versus King, is checkmate possible
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Yes it is. The scenario is applicable when there are more than these players on the board, but say we start from this position. Whites rook is on QR-1, whites king is on KR1, and blacks King is on KR-2. Confine the black King to rank 8 with your rook, and then advance your King to the 6th rank, keeping on the same file as your opponents King, till you are on the 6rank and on the same file as your opponent. Then simply move in for the kill by placing your rook at the 8 rank. CHECKMATE!!!! Any hints or revision will be welcome