Question

Calculate the ratio in which the line joining the points (–3, –1) and (5, 7) is divided by the line x = 2. Also, find the co-ordinates of the point of intersection.

Answer 1

The co-ordinates of every point on the line x = 2 will be of the type (2, y). 

Using section formula, we have:

`x = (m_1 xx 5 + m_2 xx (-3))/(m_1 + m_2)`

`2 = (5m_1 - 3m_2)/(m_1 + m_2)`

`2m_1 + 2m_2 = 5m_1 - 3m_2`

`5m_2 = 3m_1`

`m_1/m_2 = 5/3`

Thus, the required ratio is 5 : 3.

`y = (m_1 xx 7 + m_2 xx (-1))/(m_1 + m_2)`

`y = (5 xx 7 + 3 xx (-1))/(5 + 3)`

`y = (35 - 3)/8`

`y = 32/8`

`y = 4`

Thus, the required co-ordinates of the point of intersection are (2, 4).