Question

a triangle on a coordinate plane is translated according to the rule t_{-8, 4}(x, y). which is another way to write this rule?
○ (x, y) → (x + 4, y − 8)
○ (x, y) → (x − 4, y − 8)
○ (x, y) → (x − 8, y + 4)
○ (x, y) → (x + 8, y − 4)

Explanation:

Step1: Recall Translation Rule

The translation rule \(T_{a,b}(x,y)\) means we add \(a\) to the \(x\)-coordinate and \(b\) to the \(y\)-coordinate of the point \((x,y)\), so the transformation is \((x,y)\to(x + a,y + b)\).

Step2: Apply the Given Translation

For the rule \(T_{-8,4}(x,y)\), here \(a=-8\) and \(b = 4\). Substituting these values into the translation formula, we get \((x,y)\to(x+(-8),y + 4)=(x - 8,y + 4)\).

Answer:

C. \((x, y) \to (x - 8, y + 4)\)