To solve the problem of translating a point [tex]\((x, y)\)[/tex] by 3 units to the right and 2 units down, we need to understand the effect of such translations:
1. Translating 3 units to the right:
- Moving a point to the right on the Cartesian plane increases its x-coordinate.
- So, we add 3 to the x-coordinate.
2. Translating 2 units down:
- Moving a point down on the Cartesian plane decreases its y-coordinate.
- So, we subtract 2 from the y-coordinate.
Given the original point [tex]\((x, y)\)[/tex], applying these translations can be represented as:
- The new x-coordinate will be [tex]\(x + 3\)[/tex]
- The new y-coordinate will be [tex]\(y - 2\)[/tex]
Therefore, the translated point [tex]\(T(x, y)\)[/tex] can be written as:
[tex]\[
T(x, y) = (x + 3, y - 2)
\][/tex]
So, if you write the function representing the translation, the output should be:
[tex]\[
T(x, y) = (x+3, y-2)
\][/tex]
This is the function that translates the point [tex]\((x, y)\)[/tex] by 3 units to the right and 2 units down.
