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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 have
P $$(x , y) = \dfrac{m_1 x_2 + m_2x_1}{m_1 + m_2} , \dfrac{m_1 y_2 + m_2 y_1}{m_1 + m_2} $$ 
$$ x = \dfrac{m_1 x_2 + m_2x_1}{m_1 + m_2} = \dfrac{1 \times 5 + 2 \times 1}{1 + 2} = \dfrac{7}{3} $$ 
$$ y = \dfrac{m_1y_2 + m_2 y_1}{m_1 + m_2} = \dfrac{1 \times 9 + 2 \times 3}{1 + 2} = \dfrac{15}{3} = 5 $$
Hence, the co-ordinates of point P are $$ (\dfrac{7}{3} , 5) $$.

Mathematics

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