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: Calculate the change in x - coordinate

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

Step2: Calculate 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 \(-5-(-1)=-5 + 1=-4\)
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:

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