1. **Problem statement:** We need to find the distance between points A(2,3) and B(6,7), and between points C(-4,2) and D(0,-2) on a Cartesian plane. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Distance between A(2,3) and B(6,7):** - Calculate the differences: $x_2 - x_1 = 6 - 2 = 4$, $y_2 - y_1 = 7 - 3 = 4$ - Substitute into the formula: $$d = \sqrt{4^2 + 4^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \approx 5.66$$ 4. **Distance between C(-4,2) and D(0,-2):** - Calculate the differences: $x_2 - x_1 = 0 - (-4) = 4$, $y_2 - y_1 = -2 - 2 = -4$ - Substitute into the formula: $$d = \sqrt{4^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \approx 5.66$$ **Final answers:** - Distance between A and B is $4\sqrt{2} \approx 5.66$ - Distance between C and D is $4\sqrt{2} \approx 5.66$