Question

a rectangle on a coordinate plane is translated 5 units up and 3 units to the left. which rule describes the translation? (x,y)→(x + 5,y - 3) (x,y)→(x + 5,y + 3) (x,y)→(x - 3,y + 5) (x,y)→(x + 3,y + 5)

Explanation:

Step1: Analyze horizontal translation

Moving left on the \(x -\)axis. If we move \(a\) units to the left, the rule for the \(x -\)coordinate is \(x\to x - a\). Here \(a = 3\), so \(x\to x-3\).

Step2: Analyze vertical translation

Moving up on the \(y -\)axis. If we move \(b\) units up, the rule for the \(y -\)coordinate is \(y\to y + b\). Here \(b = 5\), so \(y\to y + 5\).

Answer:

\((x,y)\to(x - 3,y + 5)\) (the third option)