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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 Co-ordinates of 'M’. Hence Find the Equation of the Line Passing Through the Points C and M - Mathematics

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

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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

Concept: Equation of a Line
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