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: Recall translation rules

In a coordinate - plane, moving left/right affects the x - coordinate and moving up/down affects the y - coordinate. Moving left subtracts from the x - coordinate and moving right adds to the x - coordinate. Moving up adds to the y - coordinate and moving down subtracts from the y - coordinate.

Step2: Analyze the given translation

The rectangle is translated 3 units to the left. So, we subtract 3 from the x - coordinate of each point \((x,y)\), getting \(x-3\). It is also translated 5 units up. So, we add 5 to the y - coordinate of each point \((x,y)\), getting \(y + 5\). The translation rule is \((x,y)\to(x - 3,y+5)\).

Answer:

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