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Question
Calculate the ratio in which the line joining the points (–3, –1) and (5, 7) is divided by the line x = 2. Also, find the co-ordinates of the point of intersection.
Solution
The co-ordinates of every point on the line x = 2 will be of the type (2, y).
Using section formula, we have:
`x = (m_1 xx 5 + m_2 xx (-3))/(m_1 + m_2)`
`2 = (5m_1 - 3m_2)/(m_1 + m_2)`
`2m_1 + 2m_2 = 5m_1 - 3m_2`
`5m_2 = 3m_1`
`m_1/m_2 = 5/3`
Thus, the required ratio is 5 : 3.
`y = (m_1 xx 7 + m_2 xx (-1))/(m_1 + m_2)`
`y = (5 xx 7 + 3 xx (-1))/(5 + 3)`
`y = (35 - 3)/8`
`y = 32/8`
`y = 4`
Thus, the required co-ordinates of the point of intersection are (2, 4).
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