https://file.aiquickdraw.com/mathbot/file/1729800302756ckb24yqt.jpg

The problem asks to find the image of the point \( (1, 4) \) after a translation left by 5 units and down by 5 units.

To solve this:

1. **Translation left by 5 units:** This affects the \( x \)-coordinate. Subtract 5 from the original \( x \)-coordinate:
   \[
   x_{\text{new}} = 1 - 5 = -4
   \]

2. **Translation down by 5 units:** This affects the \( y \)-coordinate. Subtract 5 from the original \( y \)-coordinate:
   \[
   y_{\text{new}} = 4 - 5 = -1
   \]

Thus, the new point after the translation is:
\[
(-4, -1)
\]

Would you like any additional details or have further questions?

Here are 5 related questions you could explore:
1. What is the formula for a general translation of any point \( (x, y) \) by \( a \) units left and \( b \) units down?
2. How would the translation change if instead of going left, we moved right by 5 units and down by 5 units?
3. Can you explain how translations affect the overall graph of a function or shape?
4. What would the new point be if the translation was left 3 units and up 2 units from \( (1, 4) \)?
5. How do translations differ from other types of transformations like rotations or reflections?

**Tip:** When performing translations, always apply changes independently to the \( x \)- and \( y \)-coordinates.

What is the image point of (1, 4) after a translation left 5 units and down 5 units?

Find the image point after translating (1, 4) left 5 units and down 5 units. This problem focuses on coordinate geometry, applying translation formulas to adjust the x- and y-coordinates. Suitable for students in Grades 6-8.

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