1. **State the problem:** We have three identical rectangles arranged vertically in an "S" shape. 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 lies on the right edge of the middle rectangle. 2. **Understand the rectangles:** Since the rectangles are identical and stacked in an "S" shape, the total height from bottom to top is $ 12 - 4 = 8 $ units. 3. **Calculate the height of each rectangle:** There are three rectangles stacked vertically, so each rectangle has height $$ \text{height} = \frac{8}{3} = \frac{8}{3} \approx 2.67 $$ 4. **Calculate the width of each rectangle:** The width is from $ x=1 $ to $ x=7 $, so $$ \text{width} = 7 - 1 = 6 $$ 5. **Locate the middle rectangle:** The bottom rectangle spans $ y=4 $ to $ y=4 + \frac{8}{3} = \frac{20}{3} \approx 6.67 $. The middle rectangle spans from $ y=\frac{20}{3} $ to $ y=\frac{20}{3} + \frac{8}{3} = \frac{28}{3} \approx 9.33 $. 6. **Find the coordinates of point $ H $:** Point $ H $ is on the right edge of the middle rectangle, so its $ x $-coordinate is the right edge $ x=7 $. The $ y $-coordinate of $ H $ is the midpoint of the middle rectangle's vertical span: $$ y_H = \frac{\frac{20}{3} + \frac{28}{3}}{2} = \frac{48/3}{2} = \frac{16}{2} = 8 $$ 7. **Final coordinates:** $$ H = (7, 8) $$ Thus, the coordinates of point $ H $ are $ (7, 8) $.