Let the line 2x + 3y – 30 = 0 divide the join of A(3, 4) and B(7, 8) at point C(p, q) in the ratio k : 1. Then,p = \(rac{7k+3}{k+1}\), q = \(rac{8k+4}{k+1}\)As the point C lies on the line 2x + 3y – 30 = 0, it satisfies the given equation, i.e,2 x \(\bigg(rac{7k+3}{k+1}\bigg)\) + 3\(\bigg(rac{8k+4}{k+1}\bigg)\) - 30 = 0⇒ 14k + 6 + 24k + 12 – 30k – 30 = 0 ⇒ 8k – 12 = 0 ⇒ k = \(rac{12}{8}\) = \(rac{3}{2}\)∴ The line 2x + 3y – 30 = 0 divides the line joining A(3, 4) and B(7, 8) in the ratio \(rac{3}{2}\) : 1. i.e. 3 : 2 at C.Now the co-ordinates of C are \(\bigg(rac{7 imesrac{3}{2}+3}{rac{3}{2}+1},rac{8 imesrac{3}{2}+4}{rac{3}{2}+1}\bigg)\) = \(\big(rac{27}{5},rac{32}{5}\big)\).