Question

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

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 each square

• Square \(1\): It is in the second - quadrant (left - upper part). The translation \((x + 5,y-3)\) moves the figure to the right and down, so square \(1\) is not the image.
• Square \(2\): It is in the third - quadrant (left - lower part). The translation \((x + 5,y-3)\) moves the figure to the right and down, so square \(2\) is not the image.
• Square \(3\): If we assume a point \((x,y)\) of square \(LMNP\) (in the second - quadrant near the origin), after \(x+5\) (right move) and \(y - 3\) (down move), square \(3\) is in the first - quadrant (upper - right), but the \(y\) - coordinate change is not enough.
• Square \(4\): Consider a vertex of square \(LMNP\). Let's assume a vertex of \(LMNP\) has coordinates \((x,y)\). After applying the translation \((x+5,y - 3)\), moving \(5\) units to the right (positive \(x\) direction) and \(3\) units down (negative \(y\) direction) will place the square in the fourth - quadrant. Square \(4\) is in the fourth - quadrant (lower - right part)

Answer:

Square \(4\)