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: Identify \(a\) and \(b\)

Here \(a=-8\) and \(b = 4\).

Step3: Apply the rule

Substitute \(a=-8\) and \(b = 4\) into \((x,y)\to(x + a,y + b)\), we get \((x,y)\to(x-8,y + 4)\)

Answer:

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