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

Explanation:

Step1: Recall the translation rule

In a translation \(T_{a,b}(x,y)\), the rule is \((x,y)\to(x + a,y + b)\).

Step2: Substitute \(a=-8\) and \(b = 4\)

When \(a=-8\) and \(b = 4\), we have \((x,y)\to(x+(-8),y + 4)\) which simplifies to \((x,y)\to(x - 8,y + 4)\).

Answer:

\((x,y)\to(x - 8,y + 4)\) (the third option)