Question

which of the following coordinate notations describes the translation from the preimage to the image?
\bigcirc $(x, y) \to (x, y + 8)$
\bigcirc $(x, y) \to (x + 8, y)$
\bigcirc $(x, y) \to (x - 8, y)$
\bigcirc $(x, y) \to (x, y - 8)$

Explanation:

Step1: Analyze horizontal movement

Observe the x - coordinates of the pre - image (T) and image (T'). The pre - image T is to the right of the image T'. So, the x - coordinate of the image is less than the x - coordinate of the pre - image. If we let the pre - image be \((x,y)\) and the image be \((x',y')\), for horizontal translation, the change in x is \(x'=x - 8\) (since it moves 8 units to the left) and the y - coordinate remains the same (\(y' = y\)).

Step2: Match with the options

The translation rule that represents a horizontal shift of 8 units to the left (and no vertical shift) is \((x,y)\to(x - 8,y)\).

Answer:

\((x,y)\to(x - 8,y)\) (the option with this rule)