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If P ( 9a -2 , - B) Divides the Line Segment Joining a (3a + 1 , - 3 ) and B (8a, 5) in the Ratio 3 : 1 , Find the Values of a and B .

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प्रश्न

If P ( 9a -2  , - b) divides the line segment joining A (3a + 1 , - 3 ) and B (8a, 5) in the ratio 3 : 1 , find the values of a and b .

 
 
 
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उत्तर

It is given that P divides AB in the ratio 3 : 1.
Therefore, by section formula we have 

\[\Rightarrow 9a - 2 = \frac{3\left( 8a \right) + 1\left( 3a + 1 \right)}{3 + 1}\]

\[ \Rightarrow 4\left( 9a - 2 \right) = 24a + 3a + 1\]

\[ \Rightarrow 36a - 8 = 27a + 1\]

\[ \Rightarrow 9a = 9\]

\[ \Rightarrow a = 1\]

And , 

\[\Rightarrow - b = \frac{3\left( 5 \right) + 1\left( - 3 \right)}{3 + 1}\]
\[ \Rightarrow - 4b = 15 - 3\]
\[ \Rightarrow b = - 3\]

 

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अध्याय 6: Co-ordinate Geometry - Exercise 6.3 [पृष्ठ २८]

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आर.डी. शर्मा Mathematics [English] Class 10
अध्याय 6 Co-ordinate Geometry
Exercise 6.3 | Q 5 | पृष्ठ २८

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