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Find the ratio in which P (4, m) divides the line segment joining the points A (2, 3) and B (6, -3). Hence find m.

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Detailed Solution

Section formula if a point P(x, y) divides the line segment joining

A (x_{1}, y_{1}) B (x_{2}, y_{2})

in ratio of m:n
Then,

(x, y) = (\frac{{mx}_{1} + {nx}_{2}}{m + n}, \frac{{my}_{1} + {ny}_{2}}{m + n})

Let P divides AB in ratio of k:1

4 = \frac{6 k + 2}{k + 1} 4 k + 4 = 6 k + 2 k = 1

Again, using section formula;

m = \frac{- 3 \cdot k + 3 \cdot 1}{1 + 1} m = \frac{- 3 \cdot 1 + 3 \cdot 1}{1 + 1} m = 0

Correct option is 1.

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