Question

Question 7 (i)
Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.
(a) The median from A meets BC at D. Find the coordinates of point D.

Answer 1

(a) Coordinates of D can be calculated as follows:

Using section formula,
$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$,$y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$
In this case $(m_1=1,m_2=1and{x}_1=6,x_2=1,y_1=5,y_2=4)$
$x=\frac{1+6}{2}=\frac{7}{2}$
$y=\frac{4+5}{2}=\frac{9}{2}$
Therefore, coordinates of point D is $(\frac{7}{2},\frac{9}{2})$.