1. **Problem Statement:** We have four identical squares arranged in a step pattern on a coordinate grid. Points A and B are given as A(7,4) and B(27,16). We need to find the coordinates of point C, which is the lower-left corner of the third square. 2. **Understanding the setup:** Since the squares are identical and arranged in a rising step pattern, each square is shifted right and up by the same amount from the previous one. 3. **Calculate the side length of each square:** The vector from A to B covers three squares diagonally (from the first to the fourth square). The change in x is $27 - 7 = 20$ and the change in y is $16 - 4 = 12$. 4. **Find the horizontal and vertical shift per square:** Since there are 3 steps between A and B, each step in x is $\frac{20}{3}$ and each step in y is $\frac{12}{3} = 4$. 5. **Coordinates of C:** Point C is the lower-left corner of the third square, which is two steps from A (since A is the first square). So, $$x_C = 7 + 2 \times \frac{20}{3} = 7 + \frac{40}{3} = \frac{21}{3} + \frac{40}{3} = \frac{61}{3} \approx 20.33$$ $$y_C = 4 + 2 \times 4 = 4 + 8 = 12$$ 6. **Final answer:** The coordinates of point C are approximately $(20.33, 12)$ or exactly $\left(\frac{61}{3}, 12\right)$. This means point C lies about 20.33 units along the x-axis and 12 units along the y-axis.