1. **State the problem:** We have three identical rectangles arranged in an L-shape on a coordinate plane. The bottom-left corner of the lower rectangle is at $(2,3)$ and the top-right corner of the upper rectangle is at $(10,12)$. We need to find the coordinates of point $G$, which lies at the right-middle edge where the vertical middle rectangle meets the lower rectangle. 2. **Understand the rectangles:** Since the rectangles are identical, they have the same width and height. 3. **Calculate the width and height of one rectangle:** - The bottom-left corner of the lower rectangle is at $(2,3)$. - The top-right corner of the upper rectangle is at $(10,12)$. The L-shape arrangement means the total width and height cover three rectangles arranged in an L. 4. **Determine the dimensions:** - Horizontally, the total width covers two rectangles side by side. - Vertically, the total height covers two rectangles stacked. 5. **Calculate width and height of one rectangle:** - Total width = $10 - 2 = 8$ - Total height = $12 - 3 = 9$ Since two rectangles cover the width and two cover the height: - Width of one rectangle = $\frac{8}{2} = 4$ - Height of one rectangle = $\frac{9}{2} = 4.5$ 6. **Find coordinates of point $G$:** - Point $G$ is at the right-middle edge where the vertical middle rectangle meets the lower rectangle. - The lower rectangle's bottom-left corner is at $(2,3)$. - The lower rectangle's right edge is at $x = 2 + 4 = 6$. - The vertical middle rectangle is above the lower rectangle, so $G$ is at $x=6$. - The vertical middle rectangle's height is $4.5$, so its bottom edge is at $y=3 + 4.5 = 7.5$. - Point $G$ is at the middle of the right edge of the lower rectangle, so its $y$ coordinate is $3 + \frac{4.5}{2} = 3 + 2.25 = 5.25$. 7. **Final answer:** $$G = (6, 5.25)$$