Question

In what ratio does the point (0, 1) divides the line segment joining the points (-1,0) and (2, 3)?​

Answer 1

Answer :

• 2 : 1 is the required ratio.

Given :

• A(-1,0)
• B(2,3)
• C(0,1)

To find :

• In what ratio does the point C divides the line segment joining A and B.

Solution :

Using section formula:

x = [m_1x_2 + m_2x_1/m_1 + m_2]

x(0) = m_1(2) + m_2(-1)/m_1 + m_2]

=> 0 = 2m_1 - 1m_2/m_1 + m_2

=> 0(m_1 + m_2) = 2m_1 - 1m_2

=> 0 = 2m_1 - 1m_2

=> -2m_1 = -1m_2

=> 2m_1 = 1m_2

=> m_1/m_2 = 2/1

or,

y = [m_1y_2 + m_2y_1/m_1 + m_2]

y(1) = m_2(3) + m_2(0)/m_1 + m_2]

=> 1 = 3m_2 + 0m_2/m_1 + m_2

=> m_1 + m_2 = 3m_2 + 0

=> m_1 = 3m_2 - m_2

=> m_1 = 2m_2

=> m_1/m_2 = 2/1

∴ m_1 : m_2 = 2 : 1.