Question

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.

Answer 1

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