1. **State the problem:** We have three identical rectangles arranged in an L shape on the coordinate plane. The bottom-left corner of the bottom-left rectangle is at point $(1,4)$, and the top-right corner of the top-right rectangle is at point $(7,12)$. We need to find the coordinates of point $H$, which is the intersection point of the three rectangles. 2. **Understand the arrangement:** Since the rectangles are identical and arranged in an L shape, the total width and height covered by the three rectangles can be divided into segments equal to the width and height of one rectangle. 3. **Calculate the width and height of one rectangle:** - The total horizontal distance from $x=1$ to $x=7$ is $7 - 1 = 6$. - The total vertical distance from $y=4$ to $y=12$ is $12 - 4 = 8$. 4. **Determine the dimensions of one rectangle:** - Since the rectangles are identical and arranged in an L shape, the width of one rectangle is $\frac{6}{3} = 2$ (because the L shape covers 3 rectangles horizontally in total). - The height of one rectangle is $\frac{8}{2} = 4$ (because the L shape covers 2 rectangles vertically in total). 5. **Locate point $H$:** - Point $H$ is at the intersection of the three rectangles, which is at the top-right corner of the bottom-left rectangle and the bottom-left corner of the top-right rectangle. - Starting from the bottom-left corner $(1,4)$, move right by the width of one rectangle: $1 + 2 = 3$. - Move up by the height of one rectangle: $4 + 4 = 8$. 6. **Final answer:** $$H = (3, 8)$$