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 of a point \((x,y)\) is changed by \(a\) (horizontal shift) and the \(y\) - coordinate is changed by \(b\) (vertical shift).

Step2: Apply the rule for \(T_{-3,5}(x,y)\)

For \(T_{-3,5}(x,y)\), when \(a=-3\) and \(b = 5\), the new \(x\) - coordinate is \(x+a=x+(-3)=x - 3\) and the new \(y\) - coordinate is \(y + b=y+5\). So the translation rule \(T_{-3,5}(x,y)\) can be written as \((x,y)\to(x - 3,y + 5)\).

Answer:

A. \((x,y)\to(x - 3,y + 5)\)