Question

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 value of a and B

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Answer 1

Given :

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

Using section formula

$\boxed{ \rm P( x,y) = \Bigg( \dfrac{m_1x_2 + m_2x_1 }{m_1 + m_2}, \dfrac{m_1y_2 + m_2y_1 }{m_1 + m_2} \Bigg)}$

Here we have

• x₂  = 8a
• x₁  =  3a + 1
• y₂ = 5
• y₁ = -  3
• m₁ = 3
• m₂ = 1
• x = 9a - 2
• y = - b

Substituting the values in the formula

$\Rightarrow \sf P( 9a-2 \ \ , \ \ - b) = \Bigg( \dfrac{3(8a) + 1(3a + 1 )}{3 + 1} \ \ , \ \ \dfrac{3(5) + 1(-3) }{3+1 } \Bigg) \\\\\\ \Rightarrow \sf P( 9a-2 \ \ , \ \ - b) = \Bigg( \dfrac{24a + 3a + 1 }{4} \ \ , \ \ \dfrac{15- 3 }{4} \Bigg) \\\\\\ \Rightarrow \sf P( 9a-2 \ \ , \ \ - b) = \Bigg( \dfrac{27a + 1 }{4} \ \ , \ \ \dfrac{12 }{4} \Bigg) \\\\\\ \Rightarrow \sf P( 9a-2 \ \ , \ \ - b) = \Bigg( \dfrac{27a + 1 }{4} \ \ , \ \ 3 \Bigg)$

Equating x - coordinates

⇒ 9a - 2 = ( 27a + 1 )/4

⇒ 4( 9a - 2 ) = 27a + 1

⇒ 36a - 8 = 27a + 1

⇒ 36a - 27a = 1 + 8

⇒ 9a = 9

⇒ a = 1

Now equating y - coordinates

⇒ - b = 3

⇒ b = - 3

∴ the value of a is 1 and the value of b is - 3.

Answer 2

Step-by-step explanation:

⭐ QUESTION ⭐

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 value of a and B.

⭐ANSWER⭐

FORMULA USED

P(x,y)=($m_1$$x_2$+$m_2$$x_1$/$m_1$+$m_2$,$m_1$$y_2$+$m_2$$y_1$/$m_1$+$m_1$)

$m_1$=3

$m_2$=1

$x_1$=3a+1

$y_1$=-3

$x_2$=8a

$y_2$=5

$\implies P(x,y) = (\frac{3(8a + 1) + 3a + 1}{4}, \frac{3(5) + ( - 3)}{4} )$

$P = \frac{27a + 1}{4} , \frac{12}{4}$

$P = ( \frac{27a + 1}{4} ,3)$

x coordinate

$\implies$9a-2=27a+1/4

$\implies$36a-8=27a+1

$\implies$36a-27a=1+8

$\implies$9a=9

$\implies$a=9/9=1

Y coordinate

$\implies$-b=3

$\implies$b=-3