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 \(3\) units to the left. In a coordinate \((x,y)\), moving left on the \(x -\)axis means subtracting from the \(x -\)coordinate. So the \(x -\)coordinate becomes \(x-3\).

Step2: Analyze vertical translation

Moving \(5\) units up. In a coordinate \((x,y)\), moving up on the \(y -\)axis means adding to the \(y -\)coordinate. So the \(y -\)coordinate becomes \(y + 5\).

Combining these two transformations, the translation rule for the point \((x,y)\) is \((x,y)\to(x - 3,y + 5)\).

Answer:

\((x,y)\to(x - 3,y + 5)\)