Question

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 each figure

• Figure 1: Incorrect position as it is not moved \(5\) units right and \(3\) units down from \(LMNP\).
• Figure 2: Incorrect position as it is not moved \(5\) units right and \(3\) units down from \(LMNP\).
• Figure 3: Incorrect position as it is moved in the wrong direction (not \(3\) units down).
• Figure 4: Correct. If we take a vertex of square \(LMNP\) (say \(M\) which has approximate coordinates \((- 1,0)\)), after translation \(x=-1 + 5=4\) and \(y=0-3=-3\). The position of figure 4 matches the translation rule for all vertices of square \(LMNP\).

Answer:

4