What is the image point of left parenthesis, 3, comma, minus, 4, right parenthesis(3,−4) after a translation left 2 units and up 5 units?

To find the image point after a translation, you need to apply the translation to each coordinate of the original point.

The original point is \((3, -4)\).

1. **Translation left 2 units**: This means subtract 2 from the x-coordinate:
   \[
   x' = 3 - 2 = 1
   \]

2. **Translation up 5 units**: This means add 5 to the y-coordinate:
   \[
   y' = -4 + 5 = 1
   \]

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

Would you like more details on this process, or do you have any questions?

Here are 5 related questions you might find useful:
1. What is the image point of \((7, 2)\) after a translation 3 units to the right and 4 units down?
2. How do you translate a point when given a vector instead of direction and magnitude?
3. If a point \((x, y)\) is translated by \((a, b)\), what is the general formula for the new coordinates?
4. What is the effect of translating a point by \((-x, -y)\)?
5. How would you determine the original point if only the translation and image point are known?

**Tip:** In coordinate geometry, translations preserve the shape and size of geometric figures.

What is the image point of (3,−4) after a translation left 2 units and up 5 units?

Learn how to find the image point of (3,−4) after a translation of 2 units to the left and 5 units up. This problem explores translation in coordinate geometry, making it ideal for students in Grades 6-8.

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