Sure, let's tackle this problem step by step.
1. Define the translation amounts:
- We are translating the point 3 units to the right.
- We are translating the point 2 units down.
2. Starting Point:
- Let's assume our initial point is represented as [tex]\((x, y)\)[/tex].
3. Translate 3 units to the right:
- When you move a point 3 units to the right, you are effectively adding 3 to the x-coordinate.
- So the new x-coordinate will be [tex]\(x + 3\)[/tex].
4. Translate 2 units down:
- When you move a point 2 units down, you are effectively subtracting 2 from the y-coordinate.
- So the new y-coordinate will be [tex]\(y - 2\)[/tex].
Putting it all together, the new point after translating [tex]\((x, y)\)[/tex] 3 units to the right and 2 units down is [tex]\((x + 3, y - 2)\)[/tex].
Therefore, the formula for the translated point is:
[tex]\[
(x + 3, y - 2)
\][/tex]
And, for an example with initial point (0,0):
[tex]\[
(0 + 3, 0 - 2) = (3, -2)
\][/tex]
This is the result you get after translating the given point [tex]\( (x, y) \)[/tex] by 3 units to the right and 2 units down:
[tex]\[
\boxed{(x + 3, y - 2)}
\][/tex]
