Find the ratio in which the point P 3-4- 5-12 divides the line segment joining the point A 1-2- 3-2 and B 2-5

Let P ( 3/4,5/12 ) divide AB in the ration m_1:m_2 Using the section formula, we have ( 3/4,5/12 ) = [ ( 2m_1+1/2m_2/m_1+m_2 ) ] 3/4=2m_1+1/2m_2/m_1+m_2....( ...

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Byju's Answer

Standard X

Mathematics

Mid Point Formula

Find the rati...

Question

Find the ratio in which the point $P (\frac{3}{4}, \frac{5}{12})$ divides the line segment joining the point $A (\frac{1}{2}, \frac{3}{2})$ and B(2,-5)

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Solution

Let $P (\frac{3}{4}, \frac{5}{12})$ divide AB in the ration $m_{1} : m_{2}$
Using the section formula, we have
$(\frac{3}{4}, \frac{5}{12}) = [(\frac{2 m_{1} + \frac{1}{2} m_{2}}{m_{1} + m_{2}})]$
$\frac{3}{4} = \frac{2 m_{1} + \frac{1}{2} m_{2}}{m_{1} + m_{2}} . . . . (1)$
$\frac{5}{12} = \frac{- 5 m_{1} + \frac{3}{2} m_{2}}{m_{1} + m_{2}} . . . . (2)$
From (1) we have
$\frac{3}{4} = \frac{2 m_{1} + \frac{1}{2} m_{2}}{m_{1} + m_{2}}$
$3 (m_{1} + m_{2}) = 4 (2 m_{1} + \frac{1}{2} m_{2})$
$3 m_{1} + 3 m_{2} = 8 m_{1} + 2 m_{2}$
$- 5 m_{1} = - m_{2}$
$m_{1} : m_{2} = 1 : 5$

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Similar questions

Q. Question 11
Find the ratio in which the point

P (\frac{3}{4}, \frac{5}{12})

divides the line segment joining the points

A (\frac{1}{2}, \frac{3}{2})

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If true then enter

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Q. Question 5
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Find the ratio in which the point P(34,512) divides the line segment joining the point A(12,32) and B(2,-5)

Let P(34,512) divide AB in the ration m1:m2 Using the section formula, we have (34,512)=[(2m1+12m2m1+m2)] 34=2m1+12m2m1+m2....(1) 512=−5m1+32m2m1+m2....(2) From (1) we have 34=2m1+12m2m1+m2 3(m1+m2)=4(2m1+12m2) 3m1+3m2=8m1+2m2 −5m1=−m2 m1:m2=1:5

Find the ratio in which the point $P (\frac{3}{4}, \frac{5}{12})$ divides the line segment joining the point $A (\frac{1}{2}, \frac{3}{2})$ and B(2,-5)