https://file.aiquickdraw.com/mathbot/file/1726522923239b3cmgzgw.jpg

The task involves translating the given geometric figure by 6 units to the right and 4 units down. Let's follow the procedure step by step:

### Step 1: Identify the Coordinates of the Original Figure
From the image, the shape is a quadrilateral, and the coordinates of the vertices are:
1. (-7, 6)
2. (-3, 7)
3. (-5, 3)
4. (-8, 4)

### Step 2: Apply the Translation
For each point, we need to:
- Move 6 units to the right (add 6 to the x-coordinate).
- Move 4 units down (subtract 4 from the y-coordinate).

Let's calculate the new coordinates:

1. \((-7 + 6, 6 - 4) = (-1, 2)\)
2. \((-3 + 6, 7 - 4) = (3, 3)\)
3. \((-5 + 6, 3 - 4) = (1, -1)\)
4. \((-8 + 6, 4 - 4) = (-2, 0)\)

### Step 3: Plot the Translated Points
- The new coordinates of the translated figure will be:
  1. (-1, 2)
  2. (3, 3)
  3. (1, -1)
  4. (-2, 0)

You can now plot these new points and connect them to get the translated figure.

Would you like further details or have any questions?

Here are some related questions to explore:
1. What happens if we reflect the original figure over the x-axis instead of translating it?
2. How would the translation change if we moved the figure 6 units left and 4 units up instead?
3. What is the general formula for translating any point \((x, y)\) by a vector \((a, b)\)?
4. How do you calculate the area of the original and translated shapes?
5. What would happen if we rotate the original shape around the origin by 90 degrees?

**Tip:** Always double-check your calculations when applying transformations to ensure accuracy in the new positions.

Translate the figure 6 units right and 4 units down. Plot all of the points of the translated figure.

Learn how to translate a quadrilateral on a coordinate plane by moving it 6 units to the right and 4 units down. This example covers geometric translations and how to adjust the coordinates of each vertex of the figure. Suitable for students in Grades 6-8.

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