Question

A(2, 5), B(–1, 2) and C(5, 8) are the vertices of a triangle ABC, M is a point on AB such that AM : MB = 1 : 2. Find the coordinates of M. Hence find the equation of the line passing through the points C and M.

Answer 1

Let the coordinates of M be (x, y).

Thus, we have

`x = (m_1x_2 + m_2x_1)/(m_1+m_2) = (1xx(-1)+2xx2)/(1+2) = (-1+4)/3 = 3/3 = 1`

`y = (m_1y_2 + m_2y_2)/(m_1+m_2) = (1xx(2)+2xx5)/(1+2) = (2+10)/3 = 12/3 = 4`

⇒ Co-ordinates of M are (1,4).

Slope of line passing through C and M = m = `(4-8)/(1-5) = (-4)/(-4) = 1`

∴ Required equation is given by

y - 8 = 1(x - 5)

⇒ y - 8 = x - 5

⇒ y = x + 3