Question

determine the ratio in which the line 3x+5y-8=0 divides the join of (4,3), (8,7)

Answer 1

★ STRAIGHT LINES ★

$let \ \: 3x + 5y - 8 = 0 \: divides \: the \: line \: \\ joining \: a(4,3) \: and \: b(8,7) \: in \: k:1 \\ \\ intersecting \: \: line \: ab\: at \: (x,y) \\ \\ using \: section \: formula \: - \\ x = \frac{(8k + 4)}{(k + 1)} \\ \\ y = \frac{(7k + 3)}{(k + 1)} \\ \\ (x,y) \: lies \: on \: line \: 3x + 5y - 8 = 0 \\ hence \: \\ will \: satisfy \: the \: equation \\ \\ 3 \frac{(8k + 4)}{(k + 1)} + 5 \frac{(7k + 3)}{(k + 1)} - 8 = 0 \\ \\ 3(8k + 4) + 5(7k + 3) - 8(k + 1) = 0 \\ \\ 51k + 19 = 0 \\ \\ k = \frac{ - 19}{51} \\ as \: k \: is \: negative \: it \: means \: \: the \: given \: line \: divides \\ ab \: externally \: in \: 19:51$