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

Explanation:

Step1: Recall translation rules

In coordinate plane translations, moving left/right affects the \(x\)-coordinate (left: subtract, right: add) and moving up/down affects the \(y\)-coordinate (up: add, down: subtract).

Step2: Analyze horizontal (left) translation

The rectangle is translated 3 units to the left. For the \(x\)-coordinate, we subtract 3, so \(x\to x - 3\).

Step3: Analyze vertical (up) translation

The rectangle is translated 5 units up. For the \(y\)-coordinate, we add 5, so \(y\to y + 5\).

Step4: Form the translation rule

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

Answer:

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