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: Understand the translation rule notation

The rule \(T_{a,b}(x,y)\) means that the \(x\) - coordinate of a point \((x,y)\) is changed by adding \(a\) and the \(y\) - coordinate is changed by adding \(b\).

Step2: Apply the values of \(a\) and \(b\)

For the rule \(T_{-8,4}(x,y)\), when \(a=-8\) and \(b = 4\), the new \(x\) - coordinate is \(x+(-8)=x - 8\) and the new \(y\) - coordinate is \(y + 4\). So the translation rule can be written as \((x,y)\to(x - 8,y + 4)\)

Answer:

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