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प्रश्न
If P(–b, 9a – 2) divides the line segment joining the points A(–3, 3a + 1) and B(5, 8a) in the ratio 3: 1, find the values of a and b.
उत्तर
Take (x1, y1) = (–3, 3a + 1); (x2, y2) = B(5, 8a)
And (x, y) = (–b, 9a – 2)
Here m1 = 3 and m2 =1
Coordinate of P(x, y) = `((m_1x_2 + m_2x_1)/(m_1 _ m_2), (m_1y_2 + m_2y_1)/(m_1 + m_2))`
`=> x = (m_1x_2 + m_2x_1)/(m_1 _ m_2)` and `y = (m_1y_2 + m_2y_1)/(m_1 + m_2)`
`=> -b = (3 xx 5 + 1 xx (-3))/(3 + 1)` and `9a - 2 = (3xx8a + 1(3a + 1))/(3 + 1)`
`=> -b = (15 - 3)/4` and `9a - 2 = (24a + 3a + 1)/4`
`=>` –4b = 12 and 36a – 8 = 27a + 1
`=>` b = –3 and 9a = 9
a = 1 and b = –3
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