If the point P (2, 1 ) lies on the line segment joining points A (4,20 and B (8, 4) , then
(a) $A P = \frac{1}{3} A B$ (b) AP = BP (C) PB = $\frac{1}{3} A B$ (D) $A P = \frac{1}{2} A B$

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Solution

Use section formula for finding out the ratio in which P divided the line segment AB.
$(2, 1) = (\frac{m_{1} (8) + m_{2} (4)}{m_{1} + m_{2}}, \frac{m_{1} (4) + m_{2} (2)}{m_{1} + m_{2}}) \Rightarrow 2 = \frac{8 m_{1} + 4 m_{2}}{m_{1} + m_{2}}; 1 = \frac{4 m_{1} + 2 m_{2}}{m_{1} + m_{2}} \Rightarrow 3 m_{1} + m_{2} = 0 \Rightarrow \frac{m_{1}}{m_{2}} = - \frac{1}{3} ∴ t h e p o i n t P d i v i d e d A B i n r a t i o n 1 : 3 e x t e r n a l l y . A P : P B = 1 : 3 \Rightarrow A P : A B = 1 : 2 \Rightarrow A P = \frac{1}{2} A B$

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Similar questions

If the point P(2,1) lies on the line segment joining points A(4,2) and B(8,4) then

A P = \frac{1}{3} A B

A P = P B

P B = \frac{1}{3} A B

A P = \frac{1}{2} A B

P (2, 1)

A (4, 2)

B (8, 4)

P (1, 2)

A (2, 4)

B (4, 8)

\frac{A P}{A B}

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