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The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.

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#### Solution

We have given that R divides the line segment AB

AR+ RB = AB

`3/4`AB + RB = AB

⇒ RB = `"AB"/4`

⇒ AR : RB = 3 : 1

Using section formula:

`x = ((m_1x_2 + m_2x_1)/( m_1 + m_2)), y = ((m_1y_2 + m_2y_1)/(m_1 + m_2))`

m_{1} = 3, m_{2} = 1

x_{1} = - 4, y_{1} = 0

x_{2 }= 0, y_{2 }= 6

Plugging values in the formula we get

x = `( 3 xx 0 + 1 xx (- 4))/( 3 + 1), y = ( 3 xx 6 + 1 xx 0)/( 3 + 1)`

x = `(- 4)/4, y = 18/4`

⇒ x = - 1, y = `9/2`

Therefore, the coordinates of R `(-1,9/2)`

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