Question

1. select all that apply: what is the translation of \\( \triangle a b c \to \triangle d e f \\) \\( t _ { - 2,7 } \\) \\( t _ { 2,7 } \\) \\( t _ { 7, - 2 } \\) \\( ( x, y ) \to ( x - 2, y + 7 ) \\) \\( ( x, y ) \to ( x + 2, y + 7 ) \\) \\( ( x, y ) \to ( x + 7, y - 2 ) \\)

Explanation:

Step1: Find the translation rule

Assume \(A(-6,-1)\), \(B(-2,2)\), \(C(-4,-4)\), \(D(-4,6)\), \(E(0,9)\), \(F(-2,2)\)
For the \(x -\)coordinate:
Take point \(A(-6,-1)\) and \(D(-4,6)\)
\(-6 + 2=-4\)
Take point \(B(-2,2)\) and \(F(-2,2)\)
\(-2+0 = - 2\) (This is wrong. Let's use another pair. Take \(A(-6,-1)\) and \(D(-4,6)\) and \(C(-4,-4)\) and \(E(0,9)\)
For \(x\): \(-6+2=-4\), \(-4 + 2=0\)
For \(y\): \(-1+7 = 6\), \(-4+7=3\) (Wrong. Wait, correct way:
The translation formula is \((x,y)\to(x + h,y + k)\)
Take \(A(-6,-1)\) to \(D(-4,6)\)
\(-6+h=-4\Rightarrow h = 2\)
\(-1 + k=6\Rightarrow k=7\)
So the translation rule is \((x,y)\to(x + 2,y + 7)\) which can be written as \(T_{2,7}\)

Answer:

\(T_{2,7}\), \((x,y)\to(x + 2,y + 7)\)