1. **Problem Statement:** We have three identical rectangles arranged vertically and horizontally. The bottom-left corner of the bottom rectangle is at $ (1,4) $ and the top-right corner of the top rectangle is at $ (7,12) $. We need to find the coordinates of point $ H $, which is the top-right corner of the bottom rectangle and the bottom-left corner of the middle rectangle. 2. **Understanding the arrangement:** Since the rectangles are identical, they have the same width and height. 3. **Calculate total height and width:** The total height from bottom to top is $ 12 - 4 = 8 $ units. 4. **Since there are three identical rectangles arranged vertically with one on top horizontally, the vertical stack consists of two rectangles stacked vertically:** - The bottom rectangle from $ y=4 $ to $ y=4 + h $. - The middle rectangle from $ y=4 + h $ to $ y=4 + 2h $. 5. **Height of each rectangle:** Since the total vertical height of two rectangles is 8, each rectangle has height $ h = \frac{8}{2} = 4 $. 6. **Width of each rectangle:** The total width from $ x=1 $ to $ x=7 $ is $ 7 - 1 = 6 $ units. 7. **Coordinates of point $ H $:** - $ H $ is the top-right corner of the bottom rectangle, so its $ x $ coordinate is $ 1 + 6 = 7 $. - Its $ y $ coordinate is $ 4 + 4 = 8 $. Therefore, the coordinates of point $ H $ are $ (7,8) $. **Final answer:** $$ H = (7,8) $$