Question

match the following slide to its rule

Explanation:

Step1: Analyze the translation rules

• For horizontal translation: If \(x\) changes to \(x + a\), it's a shift to the left by \(|a|\) units when \(a>0\) and to the right by \(|a|\) units when \(a < 0\).
• For vertical translation: If \(y\) changes to \(y + b\), it's a shift down by \(|b|\) units when \(b>0\) and up by \(|b|\) units when \(b < 0\).

Step2: Match each rule

• For \((x,y)\to(x + 2,y-3)\):
• The \(x\) - coordinate changes as \(x\to x + 2\) (shift right by \(2\) units) and \(y\to y-3\) (shift down by \(3\) units).
• For \((x,y)\to(x - 3,y-2)\):
• The \(x\) - coordinate changes as \(x\to x-3\) (shift left by \(3\) units) and \(y\to y - 2\) (shift down by \(2\) units).
• For \((x,y)\to(x - 3,y + 5)\):
• The \(x\) - coordinate changes as \(x\to x-3\) (shift left by \(3\) units) and \(y\to y + 5\) (shift up by \(5\) units). But there is no "up \(5\), left \(3\)" match in the wrong - labeled original.
• For \((x,y)\to(x - 3,y-5)\):
• The \(x\) - coordinate changes as \(x\to x-3\) (shift left by \(3\) units) and \(y\to y-5\) (shift down by \(5\) units).
• For \((x,y)\to(x + 2,y)\):
• The \(x\) - coordinate changes as \(x\to x + 2\) (shift right by \(2\) units) and \(y\) remains the same.

Answer:

\((x,y)\to(x + 2,y-3)\) matches "Right \(2\), down \(3\)"; \((x,y)\to(x - 3,y-2)\) matches "Left \(3\), down \(2\)"; \((x,y)\to(x - 3,y-5)\) matches "Down \(5\), left \(3\)"; \((x,y)\to(x + 2,y)\) matches "Right \(2\)"