Question

the image point using the translation ((x,y) \to (x+4,y-1)) for the point ((3,3)) is:
(\bigcirc) ((7, 4)).
(\bigcirc) none of the choices are correct.
(\bigcirc) ((1, 2)).
(\bigcirc) ((7, 2)).

Explanation:

Step1: Identify the translation rule

The translation rule is \((x, y) \to (x + 4, y - 1)\). We need to apply this to the point \((3, 3)\).

Step2: Apply the x - coordinate transformation

For the x - coordinate, we use \(x+4\). Substitute \(x = 3\) into \(x + 4\), we get \(3+4=7\).

Step3: Apply the y - coordinate transformation

For the y - coordinate, we use \(y - 1\). Substitute \(y = 3\) into \(y-1\), we get \(3 - 1=2\).
So the image point of \((3,3)\) under the given translation is \((7,2)\).

Answer:

\((7, 2)\) (the option with \((7, 2)\))