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

Answer 1

(c) $\left(\frac{7}{2},\frac{9}{2}\right)$
D is the midpoint of BC.
So, the coordinates of D are
$$\begin{gathered} D\left(\frac{6+1}{2},\frac{5+4}{2}\right)\left[B\left(6,5\right)\text{and}C\left(1,4\right)\Rightarrow \left(x_1=6,y_1=5\right)\text{and}\left(x_2=1,y_2=4\right)\right] \\ \text{i.e.}D\left(\frac{7}{2},\frac{9}{2}\right) \end{gathered}$$