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 translation rule

The rule \(T_{-8,4}(x,y)\) means \(x\) - coordinate changes by \(- 8\) (left - shift) and \(y\) - coordinate changes by \(+4\) (up - shift).
For a point \((x,y)\), the new \(x\) - coordinate is \(x+(-8)=x - 8\) and the new \(y\) - coordinate is \(y + 4\).

Answer:

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