Question

Find the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.

Answer 1

Let the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by x-axis be K : 1

Therefore, the coordinates of the point of division is

x = `(m_1x_2 + m_2x_1)/(m_1 + m_2),  0 = (m_1y_2 + m_2y_1)/(m_1 + m_2)`

x = `(k (-4) + 1 (1))/(k  + 1),  0 = (k (5)+ 1 (-5))/(k + 1)`

x = `(-4k+1)/(k+1), 0 = (5k-5)/(k+1)`

x (k + 1) = -4 + 1 and 5k - 5 = 0 

k = 1 Now, x (k + 1) = -4 + 1

⇒ x (1 + 1) = -4 + 1

⇒ 2x = -3

⇒ x = `-3/2`

∴ The required ratio is k:1 = 1:1

Coordinates of P are  (x, 0) = `(-3/2,0)`