Question

Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4)?

Answer 1

Let the point be A(5, −6), B(−1, −4) and P(0, y)

Point P is on y−axis, hence its x co-ordinate is 0.So, it is of the form P(0, y)

Now, we have to find ratio.

Let the ratio be k : 1

Hence m₁ = k, m₂ = 1, x₁ = 5, y₁ = −6, x₂ = −1, y₂ = −4, x = 0, y = 0

Using sections formula x = \(\frac{m_1x_2 + m_2 x_1}{m_1 + m_2}\)

⇒ 0 = \(\frac{-k + 5}{k + 1}\)

∴ k = 5

Again y =  \(\frac{m_1y_2 + m_2 y_1}{m_1 + m_2}\)

= \(\frac{-4k - 6}{k + 1} = \frac{-20-6}{6}\) for k = 5

= \(\frac{-13}{3}\)

Hence the coordiantes of point is P(0, \(\frac{-13}{3}\)).