Question

# Calculate the co-ordinates of the point P which divides the line segment joining thr points $$A(1 , 3)$$ and $$B(5 , 9)$$ is the ratio $$1 : 2$$.

Solution

## Let's assume the co-ordinates of the point P be $$(x , y)$$Given $$A(1,3)$$ and $$B(5,9)$$Then by section formula , we haveP $$(x , y) = \dfrac{m_1 x_2 + m_2x_1}{m_1 + m_2} , \dfrac{m_1 y_2 + m_2 y_1}{m_1 + m_2}$$ $$x = \dfrac{m_1 x_2 + m_2x_1}{m_1 + m_2} = \dfrac{1 \times 5 + 2 \times 1}{1 + 2} = \dfrac{7}{3}$$ $$y = \dfrac{m_1y_2 + m_2 y_1}{m_1 + m_2} = \dfrac{1 \times 9 + 2 \times 3}{1 + 2} = \dfrac{15}{3} = 5$$Hence, the co-ordinates of point P are $$(\dfrac{7}{3} , 5)$$.Mathematics

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