Question

point P(3,b) divides the line segment AB joining the points A(1,2) and B(4,5) in the ratio 2:1 from the side of A.Find the value of b.​

Answer 1

Answer:-

Given:

P(3 , b) divides the line segment joining the points A(1 , 2) & B(4 , 5) in the ratio 2 : 1.

using section formula,

i.e., the co - ordinates of a point which divides the line segment joining the points (x₁ , y₁) & (x₂ , y₂) in the ratio m : n are :

$\sf \: (x \: , \: y) = \bigg( \dfrac{mx _{2} + nx _{1} }{m + n} \: \: , \: \: \dfrac{my _{2} + ny _{1} }{m + n} \bigg)$

Let,

• x = 3

• y = b

• x₁ = 1

• x₂ = 4

• y₁ = 2

• y₂ = 5

• m = 2

• n = 1

Hence,

$\sf \implies \: (3 \: , \: b) = \bigg( \dfrac{(2)(4)+ (1)(1) }{2 + 1} \: \:, \: \: \dfrac{(2)(5) + (1)(2) }{2 + 1} \bigg) \\ \\ \sf \implies \: (3 \: , \: b) = \bigg( \dfrac{8+ 1 }{3} \: \: ,\: \: \dfrac{10 + 2 }{3} \bigg) \\ \\ \sf \implies \: (3 \: , \: b) = \bigg( \dfrac{9}{3} \: \: ,\: \: \dfrac{12}{3} \bigg) \\ \\ \sf \implies \: (3 \: \: b) = (3 \: , \: 4) \\ \\ \sf \: On \: comparing \: both \: sides \: we \: get, \\ \\ \sf \large \implies \red{ b = 4}$

Therefore, the value of b is 4.

Answer 2

Answer:

Hope it helps you

Step-by-step explanation:

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