Question

Point P divides the line segment joining the points A(8, 0) and B(16, –8) in the ratio 3 : 5. Find its co-ordinates of point P. Also, find the equation of the line through P and parallel to 3x + 5y = 7.

Answer 1

∵ P divides AB in the ratio of 3 : 5

Let co-ordinates of P be (x, y)

∴ `x = (m_1x_2 + m_2x_1)/(m_1 + m_2)`, `y = (m_1y_2 + m_2y_1)/(m_1 + m_2)`

`x = (3 xx 16 + 5 xx 8)/(3 + 5)`, `y = (3 xx (-8) + 5 xx 0)/(3 + 5)`

`x = (48 + 40)/8 = 88/8 = 11`, `y = (-24 + 0)/8 = (-24)/8`

∴ x = 11, y = –3

∴ Co-ordinates of P be (11, –3)

Writing the line 3x + 5y = 7 in form of y = mx + c

5y = –3x + 7

`=> y = (-3)/5 x + 7/5`

∴ Slope of line m = `(-3)/5`

∴ Slope of line parallel to 3x + 5y = 7 is `(-3)/5`

∴ Required equation of line will be given by y – y₁ = m(x – x₁)

`=> y - (-3) = (-3)/5 (x - 11)`

`=> y + 3 = (-3)/5 (x - 11)`

`=>` 5y + 15 = –3x + 33

`=>` 3x + 5y = 33 – 15

`=>` 3x + 5y = 18