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

To find the image point of \((-4, 7)\) after a translation left 4 units and down 4 units, we’ll adjust the coordinates according to these directions.

1. Starting with the point \((-4, 7)\).
2. **Translation Left 4 Units**: Subtract 4 from the x-coordinate:
   \[
   -4 - 4 = -8
   \]
3. **Translation Down 4 Units**: Subtract 4 from the y-coordinate:
   \[
   7 - 4 = 3
   \]

Thus, the new coordinates are:
\[
(-8, 3)
\]

**The image point after this translation is \((-8, 3)\).**

Would you like further explanation or have any questions?

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Here are related questions you might find helpful:
1. How do we perform translations in the coordinate plane with other directions?
2. What effect do translations have on the orientation of shapes in the coordinate plane?
3. How would you translate a point by moving it diagonally in both x and y directions?
4. Can we translate points using vector notation?
5. How do translations differ from other transformations like rotations and reflections?

**Tip:** Always check if the direction is positive (right/up) or negative (left/down) before translating each coordinate!

What is the image point of (-4,7) after a translation left 4 units and down 4 units?

Learn how to find the image point of (-4,7) after translating it left by 4 units and down by 4 units. This problem explores fundamental concepts of coordinate geometry, including translation rules, and provides a clear solution. Ideal for middle school students in Grades 6-8.

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