What is the image point of left parenthesis, 9, comma, 9, right parenthesis(9,9) after a translation right 5 units and down 4 units?

To find the image point of \((9,9)\) after translating right 5 units and down 4 units, we modify the \(x\)- and \(y\)-coordinates accordingly:

1. **Translation right by 5 units**: This means adding 5 to the \(x\)-coordinate.
   \[
   x = 9 + 5 = 14
   \]

2. **Translation down by 4 units**: This means subtracting 4 from the \(y\)-coordinate.
   \[
   y = 9 - 4 = 5
   \]

Thus, the image point is:
\[
(14, 5)
\]

Would you like further details on how translations work or any other related concept?

Here are 5 related questions for deeper exploration:
1. What is the effect of translating a point left or right on the coordinate plane?
2. How do vertical translations affect the \(y\)-coordinates of points?
3. What happens to a point if it's translated both horizontally and vertically?
4. Can you find the image of a point after multiple successive translations?
5. How does translation differ from rotation or reflection in geometry?

**Tip**: Translations only affect the position of a point, not its orientation or size, making them a form of **rigid transformation**.

What is the image point of (9,9) after a translation right 5 units and down 4 units?

Learn how to find the image of point (9,9) after translating it right by 5 units and down by 4 units. This detailed solution explains key geometric concepts of translation on a coordinate plane, using the translation formula. Suitable for students in Grades 6-8.

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