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

Explanation:

Step1: Understand Translation Rule

The translation rule \( T_{a,b}(x,y) \) means we add \( a \) to the \( x \)-coordinate and \( b \) to the \( y \)-coordinate, i.e., \( (x,y) \to (x + a, y + b) \). Here, the rule is \( T_{-8,4}(x,y) \), so \( a=-8 \) and \( b = 4 \).

Step2: Apply the Rule

Substitute \( a=-8 \) and \( b = 4 \) into the translation formula. So \( x \) becomes \( x+(-8)=x - 8 \) and \( y \) becomes \( y + 4 \). Thus, the translation rule is \( (x,y)\to(x - 8,y + 4) \).

Answer:

\((x,y)\to(x - 8,y + 4)\) (the first option among the given ones with this rule)