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The diagram shows three identical rectangles and we are asked to find the coordinates of point H.

### Step-by-step solution:

1. **Identify the dimensions of the rectangle**: 
   Since the rectangles are identical, we can determine the width and height by looking at the coordinates provided.
   
   - The bottom-left rectangle starts at (1, 4) and the top-right rectangle ends at (7, 12). This indicates a total horizontal span of 6 units (from 1 to 7) and a vertical span of 8 units (from 4 to 12).

   - Given there are three rectangles stacked vertically and horizontally, let's assume each rectangle has a width of 6 units divided by 2 and a height of 8 units divided by 3, as they form this block structure.

2. **Rectangle dimensions**:
   - **Width**: \( \frac{6}{2} = 3 \) units.
   - **Height**: \( \frac{8}{3} \approx 2.67 \) units.

3. **Locate point H**: 
   Point H appears where the middle rectangle connects with the bottom rectangle. To find its coordinates:
   
   - Horizontally: The x-coordinate of point H is the same as that of the bottom-left corner of the middle rectangle, which is located at \( 1 + 3 = 4 \). Thus, \( x_H = 4 \).

   - Vertically: Point H lies on the top of the bottom rectangle, which means we add the height of one rectangle to the y-coordinate of the bottom-left corner (1, 4). So, the y-coordinate of point H is \( 4 + \frac{8}{3} = 6.67 \approx 6 \).

### Conclusion:
The approximate coordinates of point H are \( (4, 6) \).

Would you like more details, or do you have any questions? Here are some related questions to expand on this topic:

1. How can you verify the dimensions of each rectangle given only the outer coordinates?
2. What method would you use to ensure identical shapes in such problems?
3. How would you calculate the midpoint of a rectangle given its coordinates?
4. How can you generalize the coordinates of any point on a rectangular grid?
5. Can you solve for the area of each rectangle given their dimensions?

**Tip**: Always check if the shapes are proportional when dealing with stacked or connected geometric figures.

The three rectangles shown below are identical. Work out the coordinates of point H.

Discover how to calculate the coordinates of point H in a series of three identical rectangles, using coordinate geometry and rectangle properties. This step-by-step solution covers key geometric concepts, perfect for students in Grades 6-8.

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