Question

identifying a translation
assume each figure shown has the same orientation.
which figure is the image of square lmnp after a
translation of
$(x,y)\to(x + 5,y - 3)$?

Explanation:

Step1: Analyze the translation rule

The translation rule is \((x,y)\to(x + 5,y-3)\). This means that each point of the square \(LMNP\) is moved \(5\) units to the right (because \(x\) - coordinate is increased by \(5\)) and \(3\) units down (because \(y\) - coordinate is decreased by \(3\)).

Step2: Check the position of square \(LMNP\) and the translated square

Square \(LMNP\) is in the second quadrant. After a translation of \(5\) units to the right (adding \(5\) to the \(x\) - coordinate) and \(3\) units down (subtracting \(3\) from the \(y\) - coordinate), we look at the positions of the numbered squares.
Square \(4\) is \(5\) units to the right and \(3\) units down relative to square \(LMNP\) (assuming we consider the center or a vertex of the square for the coordinate - based movement).

Answer:

Figure \(4\)