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Question
Find the ratio in which the line segment joining the points A(6, 3) and B(–2, –5) is divided by x-axis.
Solution
As we know that,
at x-axis, y = 0
∴ point will be P(x, 0)
and let the ratio be k : 1
then `((m_1x_2 + m_2x_1)/(m_1 + m_2), (m_1y_2 + m_2y_1)/(m_1 + m_2))` = (x, 0)
`\implies ((-2k + 6)/(k + 1), (-5k + 3)/(k + 1))` = (x, 0)
∴ `(-5k + 3)/(k + 1)` = 0
`\implies` –5k + 3 = 0
`\implies` k = `3/5`
So, required ratio is 3 : 5.
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