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: Understand horizontal translation

Moving left on the coordinate - plane means subtracting from the x - coordinate. Translating 3 units to the left changes the x - coordinate from \(x\) to \(x - 3\).

Step2: Understand vertical translation

Moving up on the coordinate - plane means adding to the y - coordinate. Translating 5 units up changes the y - coordinate from \(y\) to \(y + 5\).

Step3: Determine the translation rule

The rule for the translation of a point \((x,y)\) 3 units to the left and 5 units up is \((x,y)\to(x - 3,y + 5)\).

Answer:

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