If A(4, 2), B(6, 5) and C(1, 4) be the vertices of ∆ABC and AD is median, then the coordinates of D are
Question:

If A(4, 2), B(6, 5) and C(1, 4) be the vertices of ∆ABC and AD is median, then the coordinates of D are

(a) $\left(\frac{5}{2}, 3\right)$

(b) $\left(5, \frac{7}{2}\right)$

(C) $\left(\frac{7}{2}, \frac{9}{2}\right)$

(d) None of these

Solution:

(c) $\left(\frac{7}{2}, \frac{9}{2}\right)$

D is the midpoint of BC.
So, the coordinates of D are

$D\left(\frac{6+1}{2}, \frac{5+4}{2}\right) \quad\left[B(6,5)\right.$ and $C(1,4) \Rightarrow\left(x_{1}=6, y_{1}=5\right)$ and $\left.\left(x_{2}=1, y_{2}=4\right)\right]$

i.e. $D\left(\frac{7}{2}, \frac{9}{2}\right)$