The line segment joining the points $ (1,2) $ and $ (k, 1) $ is divided by the line $ 3 x+4 y-7=0 $ in the ratio $ 4: 9 $, then $ k $ is

Question

The line segment joining the points $ (1,2) $ and $ (k, 1) $ is divided by the line $ 3 x+4 y-7=0 $ in the ratio $ 4: 9 $, then $ k $ is, $ -2 $, $ 2 $, $ -3 $, $ 3 $

MARKS App · Accepted Answer

Using section formula, we can write the point of division has the coordinates 4 k + 9 4 + 9 , 4 + 9 × 2 4 + 9 = 4 k + 9 13 , 22 13 This point must lie in the given line. So, 3 × 4 k + 9 13 + 4 × 22 13 - 7 = 0 ⇒ 3 × 4 k + 9 13 = 3 13 ⇒ k = - 2

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