1. **State the problem:** We need to find the distance between two points $A$ and $B$ on a Cartesian plane. 2. **Formula:** The distance between points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **First graph points:** $A(1, 2)$ and $B(7, 7)$. Calculate the differences: $$x_2 - x_1 = 7 - 1 = 6$$ $$y_2 - y_1 = 7 - 2 = 5$$ 4. **Calculate distance for first graph:** $$d = \sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61} \approx 7.8$$ 5. **Second graph points:** $A(2, 9)$ and $B(6, 1)$. Calculate the differences: $$x_2 - x_1 = 6 - 2 = 4$$ $$y_2 - y_1 = 1 - 9 = -8$$ 6. **Calculate distance for second graph:** $$d = \sqrt{4^2 + (-8)^2} = \sqrt{16 + 64} = \sqrt{80} \approx 8.9$$ **Final answers:** - Distance $AB$ for first graph is approximately $7.8$ units. - Distance $AB$ for second graph is approximately $8.9$ units.