Question

find the co-ordinates of the point p, which divides the line joining A (0,0) and B (5,10) in the ratio​ of 2:3​

Answer 1

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Find the co-ordinates of the point p, which divides the line joining A (0,0) and B (5,10) in the ratio of 2:3.

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➺ P ( x, y) = ( 2 , 4 )

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$\sf 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: p \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3 \\ \sf A•┈────┈ ╌•╌────┈┈•B \\ \sf (0, 0 ) \: \: \: \: \: \: \: \: \: \: \: \: ( x, y) \: \: \: \: \: \: \: \: \: \: \: ( 5 , 10 )$

$\sf \: Let , P = ( x, y) , \: \: A( x_1 , y_1 ) = ( 0 ,0) , B ( x _2 , y_2 ) =(5,10) \\ \sf \: and \: \: \: m_1 = 2 , m_2 = 3$

$\sf \: P ( x, y) = P (\frac{m_1 x_2 + m_2x_1}{ m_1 + m_2} , \frac{m_1 y_2 + m_2y_1 }{m_1 + m_2})$

$\sf \: P ( x, y) = (\frac{2×5+3×0}{2+3},\frac{2×10+3×0}{2+3})$

$\sf \: P (x, y) = (\frac{10}{5} ,\frac{20}{5})$

$\sf \: P ( x, y) = ( 2 , 4 )$

➺ Hence , the co - ordinates of points P is ( 2 , 4 ) .

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Answer 2

Answer:

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