Question

Find the ratio in which the line segment joining the points A(6, 3) and B(–2, –5) is divided by x-axis.

Answer 1

As we know that,

at x-axis, y = 0

∴ point will be P(x, 0)

and let the ratio be k : 1

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

`\implies ((-2k + 6)/(k + 1), (-5k + 3)/(k + 1))` = (x, 0)

∴ `(-5k + 3)/(k + 1)` = 0

`\implies` –5k + 3 = 0

`\implies` k = `3/5`

So, required ratio is 3 : 5.