Question

you can transform $\triangle ghi$ to $\triangle ghi$ by translating it and then performing a dilation centered at the origin. so, $\triangle ghi \sim \triangle ghi$. find the translation rule and the scale factor of the dilation.
simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.
translation: $(x, y) \to (\square, \square)$
scale factor:

Explanation:

Step1: Identify coordinates of vertices

Coordinates:
$G(5, -8)$, $H(7, -6)$, $I(5, -4)$
$G'(-10, -10)$, $H'(0, 0)$, $I'(-10, 10)$

Step2: Find translation rule

Take point $H(7, -6)$ to $H'(0,0)$.
Solve $7 + a = 0$, $-6 + b = 0$
$a = -7$, $b = 6$
Translation: $(x,y)\to(x-7, y+6)$
Verify with $G$: $5-7=-2$, $-8+6=-2$; translated $G$ is $(-2,-2)$

Step3: Find scale factor

Use translated $G(-2,-2)$ and $G'(-10,-10)$.
Scale factor $k=\frac{-10}{-2}=2$
Verify with $I$: translated $I$ is $5-7=-2$, $-4+6=2$; $-2\times2=-10$, $2\times2=10$ (matches $I'$)

Answer:

Translation: $(x, y) \mapsto (x - 7, y + 6)$
Scale factor: $2$