Question

In what ratio is the line segment joining the points (3, −5) and (−1, 6) divided by the line y = x? 

Answer 1

When the line segment

Let Ratio

m₁ : m₂ = K : 1

Divide the line segment in the ratio K : 1 using the coordinates P(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 = `(K(-1) + 1 xx 3)/(K + 1),  y = (K xx 6 - 1 xx 5)/(K + 1)`

x = `(-K + 3)/(k + 1),  y = (6K - 5)/(K + 1)`

Given line y = x

Put the value of x and y in the equation of line

`(-K + 3)/(K + 1) = (6K - 5)/(k + 1)`

⇒ −k + 3 = 6k − 5

⇒ −K −6K = −5 − 3

⇒ 7K = 8

K = `8/7`