Question

translate a figure
construct the image of
△efg after the following
transformation:
t₆,-1
e(-8,-1) f(0,2) g(-3,-8)

1. drag the correct answer to

the correct point.
(9, -7)
(14, 0)
(3, -9)
(6, 2)
(6, -3)
(-2, 0)
(-2, -2)
(6, 1)
(-9, -9)
e(?,?)
answer by dragging items
here
f(?,?)
answer by dragging items
here
g(?,?)
answer by dragging items
here

Explanation:

Step1: Understand the translation rule

The translation \(T_{6,-1}\) means we add \(6\) to the \(x -\)coordinate and subtract \(1\) from the \(y -\)coordinate of each point.
For a point \((x,y)\), the translated point is \((x + 6,y-1)\)

Step2: Translate point \(E(-8,1)\)

For \(E(-8,1)\), using the rule \((x + 6,y - 1)\):
\(x=-8\), \(y = 1\)
\(x+6=-8 + 6=-2\)
\(y-1=1-1 = 0\)
So \(E'(-2,0)\)

Step3: Translate point \(F(0,2)\)

For \(F(0,2)\), using the rule \((x + 6,y - 1)\):
\(x = 0\), \(y=2\)
\(x+6=0 + 6=6\)
\(y-1=2-1=1\)
So \(F'(6,1)\)

Step4: Translate point \(G(-3,8)\)

For \(G(-3,8)\), using the rule \((x + 6,y - 1)\):
\(x=-3\), \(y = 8\)
\(x+6=-3+6 = 3\)
\(y-1=8 - 1=7\)
But wait, there is a mistake. Let's re - check.
Wait, no! Wait the original \(G\) point: if \(G(-3,-8)\) (assuming a typo in the problem statement, because if \(G(-3,8)\) is not in the options. If \(G(-3,-8)\))
For \(G(-3,-8)\), \(x=-3\), \(y=-8\)
\(x + 6=-3+6=3\)
\(y-1=-8-1=-9\)
So \(G'(3,-9)\)

Answer:

\(E'(-2,0)\), \(F'(6,1)\), \(G'(3,-9)\)