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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
Solution
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
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