The equation of the median of the triangle with the vertices $(4, 3), (- 2, 3), (1, - 2)$ passing through the point $(- 2, 3)$ is

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5 x + 9 y - 17 = 0

9 x - 5 y - 11 = 0

5 x + 9 y - 11 = 0

5 x - 9 y + 13 = 0

answer is A.

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Detailed Solution

Let $E$ is the midpoint of $A (4, 3)$ and $C (1, - 2)$ is $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

$= (\frac{4 + 1}{2}, \frac{3 - 2}{2})$

$= (\frac{5}{2}, \frac{1}{2})$

Equation of $B (- 2, 3)$ and $(\frac{5}{2}, \frac{1}{2})$ is

$\frac{y - y_{1}}{y_{1} - y_{2}} = \frac{x - x_{1}}{x_{1} - x_{2}}$

$\frac{y - 3}{3 - \frac{1}{2}} = \frac{x + 2}{- 2 - \frac{5}{2}}$

$\frac{y - 3}{(\frac{5}{2})} = \frac{x + 2}{(\frac{- 9}{2})}$

$- \frac{9}{2} y + \frac{27}{2} = \frac{5}{2} x + 5$

$\frac{5}{2} x + \frac{9}{2} y + 5 - \frac{27}{2} = 0$

$5 x + 9 y + 10 - 27 = 0$

$5 x + 9 y - 17 = 0$

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