Question

triangle efg has vertices e(-3,4), f(-5,-1), and g(1,1). the triangle is translated so that the coordinates of the image are e(-1,0), f(-3,-5), and g(3,-3). which rule was used to translate the image? t_{4,-4}(x,y) t_{-4,-4}(x,y) t_{2,-4}(x,y) t_{-2,-4}(x,y)

Explanation:

Step1: Find the change in \(x\) - coordinate

For point \(E(-3,4)\) and \(E'(-1,0)\), the change in \(x\) is \(-1-(-3)=2\).
For point \(F(-5, - 1)\) and \(F'(-3,-5)\), the change in \(x\) is \(-3-(-5)=2\).
For point \(G(1,1)\) and \(G'(3,-3)\), the change in \(x\) is \(3 - 1=2\).

Step2: Find the change in \(y\) - coordinate

For point \(E(-3,4)\) and \(E'(-1,0)\), the change in \(y\) is \(0 - 4=-4\).
For point \(F(-5,-1)\) and \(F'(-3,-5)\), the change in \(y\) is \(-5-(-1)=-4\).
For point \(G(1,1)\) and \(G'(3,-3)\), the change in \(y\) is \(-3 - 1=-4\).

The translation rule \(T_{a,b}(x,y)=(x + a,y + b)\), where \(a = 2\) and \(b=-4\)

Answer:

\(T_{2,-4}(x,y)\)