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Question
Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Solution 1
Suppose the point (-1, 6) divides the given line segment in the ratio m1: m2 and the coordinates of the ends of the line segment are (-3, 10) and (6, -8).
`x = (m_1x_2 + m_2x_1)/(m_1 + m_2)`
`-1 = (m_1 xx 6 + m_2 xx (-3))/(m_1 + m_2)`
⇒ 6m1 - 3m2 = -m1 - m2
⇒ 6m1 + m1 = 3m2 - m2
⇒ 7m1 = 2m2
⇒ `"m"_1/"m"_2 = 2/7`
⇒ m1 : m2 = 2 : 7
Therefore, the required ratio is 2:7.
Solution 2
Let the ratio in which the line segment joining (-3, 10) and (6, -8) is divided by point (-1, 6) be k : 1.
Therefore, -1 = `(6k-3)/(k+1)`
-k - 1 = 6k -3
7k = 2
k = `2/7`
Therefore, the required ratio is 2:7.
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