Question

a triangle on a coordinate plane is translated according to the rule ( t_{-3,5}(x,y) ). which is another way to write this rule?
( (x,y)\to(x - 3,y + 5) )
( (x,y)\to(x - 3,y - 5) )
( (x,y)\to(x + 3,y - 5) )
( (x,y)\to(x + 3,y + 5) )

Explanation:

Step1: Recall the translation rule

In a translation \(T_{a,b}(x,y)\), the \(x -\)coordinate is changed by \(a\) and the \(y -\)coordinate is changed by \(b\). That is, the rule is \((x,y)\to(x + a,y + b)\).

Step2: Substitute \(a=-3\) and \(b = 5\)

When \(a=-3\) and \(b = 5\), we substitute into the formula \((x,y)\to(x + a,y + b)\).
For the \(x -\)coordinate: \(x+a=x+(-3)=x - 3\).
For the \(y -\)coordinate: \(y + b=y+5\).

Answer:

\((x,y)\to(x - 3,y + 5)\) (the first option)