Math, asked by taranjeetkau491, 7 months ago

the point (4,2) divided the line segment. joining (5,1) and (2,y) in ratio 1:2 find y

Answers

Answered by VishnuPriya2801
34

Answer:-

Given:

The point (4 , 2) divided the line segment joining the points (5 , 1) & (2 , y) in the ratio 1 : 2.

Using section formula ;

i.e., the point which divides the line segment joining the points  \sf (x_1 , y_1) \:\: \& (x_2 , y_2) in the ratio m : n is :

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

Let,

  •  \sf x_1 = 5

  •  \sf x_2 = 2

  •  \sf y_1 = 1

  •  \sf y_2 = y

  • m = 1

  • n = 2

Hence,

  \sf \implies(4 \: , \:2 ) =  \bigg( \dfrac{(1)(2) + (2)(5)}{1 + 2} \:  \:,  \:  \:   \dfrac{(1)(y) +(2)(1) }{1 + 2}  \bigg) \\  \\  \sf \implies \: (4 \: , \: 2) =  \bigg( \dfrac{2 + 10}{3}   \:  \: , \:  \:  \dfrac{y + 2}{3}  \bigg) \\  \\  \implies \sf(4 \:  ,\: 2) =  \bigg( \dfrac{12}{3}  \:  \: , \:  \:  \dfrac{y + 2}{3}  \bigg)

On comparing both sides we get,

4 = 12/3.

→ 4 = 4

And,

 \sf \implies \: 2 =  \frac{y + 2}{3} \\  \\  \sf \implies \: 6 = y + 2 \\  \\  \sf \implies \: y = 6 - 2 \\  \\

→ y = 4

Hence, the value of y is 4.

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