1. The problem asks for the length of a line segment with endpoints at coordinates $(1,2)$ and $(5,6)$ on the Cartesian plane. 2. To find the length of a line segment between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the distance formula: $$\text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. Substitute the given points into the formula: $$\sqrt{(5 - 1)^2 + (6 - 2)^2} = \sqrt{4^2 + 4^2} = \sqrt{16 + 16}$$ 4. Simplify the square root: $$\sqrt{32} = \sqrt{16 \times 2} = 4 \sqrt{2}$$ 5. Approximate $4 \sqrt{2}$ if needed: $4 \times 1.414 = 5.656$, which is closest to answer choice B (5). Therefore, the length of the line segment is $4\sqrt{2}$, approximately 5, so the correct choice from the options is **B 5**.