1. **Problem statement:** Find the coordinates of point B given that point P(3, 5) divides the line segment joining A(2, 4) and B in the ratio 1:1 internally. 2. **Formula used:** If a point P divides the line segment AB in the ratio $m:n$ internally, then the coordinates of P are given by: $$P = \left( \frac{m x_B + n x_A}{m+n}, \frac{m y_B + n y_A}{m+n} \right)$$ 3. **Given:** - $A = (2, 4)$ - $P = (3, 5)$ - Ratio $m:n = 1:1$ 4. **Apply the formula:** Since $m = n = 1$, the coordinates of P are the midpoint of A and B: $$3 = \frac{1 \cdot x_B + 1 \cdot 2}{1+1} = \frac{x_B + 2}{2}$$ $$5 = \frac{1 \cdot y_B + 1 \cdot 4}{1+1} = \frac{y_B + 4}{2}$$ 5. **Solve for $x_B$ and $y_B$:** Multiply both equations by 2: $$6 = x_B + 2 \implies x_B = 6 - 2 = 4$$ $$10 = y_B + 4 \implies y_B = 10 - 4 = 6$$ 6. **Answer:** The coordinates of point B are $\boxed{(4, 6)}$.