If x-2y+k+0 is a median of the triangle whose vertices are at points A(-1 ,3) B(0, 4) and C(-5, 2) find the value of k.

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Solution

The coordinates of the centroid G of $△$ ABC are
$(\frac{- 1 + 0 - 5}{3}, \frac{3 + 4 + 2}{3}) i . e ., (- 2, 3)$
Since G lies on the median x-2y+k+0. So, coordinates of G satisfy its equation.
$∴ - 2 - 6 + k = 0 \Rightarrow k = 8$ .

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