If the vertices of a triangle ABC are A(1, 2, 1), B(4, 2, 3) and C(2, 3, 1), then the equation of the median passing through the vertex A, is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{x-1}{2}=2y-4=z-1\)
The median through A joins A to the midpoint D of BC:
\( \displaystyle D = \left(\frac{4+2}{2}, \frac{2+3}{2}, \frac{3+1}{2}\right) = \left(3, \frac{5}{2}, 2\right) \)
Direction ratios of AD:
\( \displaystyle 3 - 1,\ \frac{5}{2} - 2,\ 2 - 1 = 2,\ \frac{1}{2},\ 1 \)
The line through A(1, 2, 1) with these direction ratios is
\( \displaystyle \frac{x-1}{2} = \frac{y-2}{\frac{1}{2}} = \frac{z-1}{1} \)
Since \(\frac{y-2}{1/2} = 2(y-2) = 2y - 4\):
\( \displaystyle \frac{x-1}{2} = 2y - 4 = z - 1 \)