Answer:
![T_{ - 5 ,8} \: or \: D'(x,y) →D(x - 5,y + 8)](https://tex.z-dn.net/?f=T_%7B%20-%205%20%2C%3C%2Fp%3E%3Cp%3E8%7D%20%5C%3A%20or%20%5C%3A%20D%27%28x%2Cy%29%20%E2%86%92D%28x%20-%205%2Cy%20%2B%208%29)
Step-by-step explanation:
![T _ { ? ,?}](https://tex.z-dn.net/?f=T%20_%20%7B%20%3F%20%2C%3C%2Fp%3E%3Cp%3E%3F%7D)
![D'(x,y) →D(x \pm ?,y \pm ?)](https://tex.z-dn.net/?f=D%27%28x%2Cy%29%20%E2%86%92D%28x%20%5Cpm%20%3F%2Cy%20%5Cpm%20%3F%29)
given D : (7,-3), and D' : (2,5)
the coordinates of D can be represented as (x1,y1), and the coordinates of D' can be represented as (x,y).
you can simply take the difference in the x values and difference in the y values from the preimage to image.
like this:
f'(x,y) → f(x+(x-x1),y+(y-y1)) : ![T _ {(x-x_1),(y-y_1)}](https://tex.z-dn.net/?f=%3C%2Fp%3E%3Cp%3ET%20_%20%7B%28x-x_1%29%2C%28y-y_1%29%7D)
D'(x,y) → D(x+(2-7),y+(5--3))
D'(x,y) → D(x<u>-5</u>,y<u>+8</u>) : ![T _ {-5 ,8}](https://tex.z-dn.net/?f=%3C%2Fp%3E%3Cp%3ET%20_%20%7B-5%20%2C8%7D)