What is the image point of left parenthesis, minus, 7, comma, 0, right parenthesis(−7,0) after a translation left 4 units and up 1 unit?

To find the image point of \((-7, 0)\) after a translation left 4 units and up 1 unit, you can follow these steps:

1. **Translation Left 4 Units**: Subtract 4 from the x-coordinate.
   \[
   x = -7 - 4 = -11
   \]

2. **Translation Up 1 Unit**: Add 1 to the y-coordinate.
   \[
   y = 0 + 1 = 1
   \]

Therefore, the image point after the translation is \((-11, 1)\).

Would you like more details or have any questions?

Here are some related questions you might find useful:
1. What is the image of the point (3, -2) after translating it right 5 units and down 3 units?
2. How do you find the image of a point after a reflection over the y-axis?
3. What is the general formula for translating a point in the coordinate plane?
4. How would you translate a point by a vector \(\langle a, b \rangle\)?
5. What is the effect of translating a point by \((0, 0)\) on the coordinate plane?

**Tip:** When translating a point, remember that left and right affect the x-coordinate, while up and down affect the y-coordinate.

Discover how to find the image point of (-7, 0) after a translation left 4 units and up 1 unit in the coordinate plane. This problem explores coordinate geometry concepts related to translations. Suitable for Grades 6-8.

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