What is the image point of left parenthesis, minus, 1, comma, minus, 5, right parenthesis(−1,−5) after a translation left 1 unit and up 4 units?

To find the image point of \((-1, -5)\) after a translation left 1 unit and up 4 units, follow these steps:

1. **Translation Left 1 Unit**: Subtract 1 from the x-coordinate.
   \[
   x = -1 - 1 = -2
   \]

2. **Translation Up 4 Units**: Add 4 to the y-coordinate.
   \[
   y = -5 + 4 = -1
   \]

Therefore, the image point after the translation is \((-2, -1)\).

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 (2, 3) after translating it right 2 units and down 2 units?
2. How do you find the image of a point after a reflection over the x-axis?
3. What is the general formula for translating a point left and up by given units?
4. How would you translate a point by a vector \(\langle -2, 5 \rangle\)?
5. What happens to a point when you translate it left and down by the same number of units?

**Tip:** When translating a point, always adjust the coordinates according to the direction: left/right changes the x-coordinate, and up/down changes the y-coordinate.

Learn how to find the image point of (-1, -5) after a translation left 1 unit and up 4 units with detailed step-by-step instructions. This problem involves coordinate geometry and translation concepts, suitable for Grades 7-9 students.

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