What is the image point of left parenthesis, 5, comma, 1, right parenthesis(5,1) after a translation right 5 units and down 2 units?

To find the image of the point \((5, 1)\) after a translation, you apply the given transformations to the original coordinates:

1. **Right 5 units:** Add 5 to the x-coordinate.
2. **Down 2 units:** Subtract 2 from the y-coordinate.

Starting with the point \((5, 1)\):
- **x-coordinate:** \(5 + 5 = 10\)
- **y-coordinate:** \(1 - 2 = -1\)

So, the image point after the translation is \((10, -1)\).

Would you like more details or have any questions about this? Here are 5 related questions to deepen your understanding:

1. What is the image of the point \((0, 0)\) after the same translation?
2. How do you express translations as a function or in vector form?
3. What happens to a point if you translate it left by a negative number of units?
4. How do translations differ from other transformations like rotations and reflections?
5. What is the inverse of a translation?

**Tip:** Translations only shift points; they do not change the shape or size of figures.

What is the image point of (5, 1) after a translation right 5 units and down 2 units?

Learn how to find the image of the point (5, 1) after a translation of 5 units to the right and 2 units down. This geometry problem involves key concepts of coordinate transformations, suitable for students in Grades 5-6.

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