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Question
In what ratio is the join of (4, 3) and (2, –6) divided by the x-axis? Also, find the co-ordinates of the point of intersection.
Solution
Let P(x, 0) be the point of intersection which divides the line joining the points A(4, 3), B(2, –6) in the ratio of m1 : m2
∴ `x = (m_1 xx 2 + m_2 xx 4)/(m_1 + m_2)`
= `(2m_1 + 4m_2)/(m_1 + m_2)` ....(i)
And `0 = (m_1 xx (-6) + m_2(3))/(m_1 + m_2)`
`\implies` – 6m1 + 3m2 = 0
`\implies` 3m2 = 6m1
`\implies m_1/m_2 = 3/6 = 1/2`
∴ Required ratio be m1 : m2 = 1 : 2
Now, substituting the value of m1 and m2 in (i); we have
`x = (1 xx 2 + 2 xx 4)/(1 + 2)`
= `(2 + 8)/3`
= `10/3`
∴ Required point of intersection is `(10/3, 0)`
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