The line 2x + y – 4 = 0 divides the line segment joining A(2, –2) and B(3, 7) in the ratio

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2 : 9 Explanation: Let P be the intersection. Parametrize P = A + t(B – A) = (2 + t, –2 + 9t) Substitute in 2x + y – 4 = 0: 2(2 + t) + (–2 + 9t) – 4 = 11t – 2 = 0 $\Rightarrow$ t = $\frac{2}{11}$ So, AP : PB = t : (1 – t) = $\frac{2}{11}$ : $\frac{9}{11}$ = 2 : 9

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