Question

write the rule for this translation: slide 3 up and 2 right
(x,y)---->(x - 2,y + 3)
(x,y)---->(x + 3,y + 2)
(x,y)---->(x + 2,y + 3)

Explanation:

Step1: Recall translation rules

For a translation, moving right \(a\) units means \(x\) - coordinate increases by \(a\) (i.e., \(x\to x + a\)), and moving up \(b\) units means \(y\) - coordinate increases by \(b\) (i.e., \(y\to y + b\)).

Step2: Apply the given movement

We need to slide 2 right and 3 up. So for a point \((x,y)\), the new \(x\) - coordinate is \(x+2\) (because moving right 2 units) and the new \(y\) - coordinate is \(y + 3\) (because moving up 3 units). So the translation rule is \((x,y)\to(x + 2,y+3)\).

Answer:

\((x,y)\to(x + 2,y + 3)\) (the third option: \((x,y)\to(x + 2,y + 3)\))