Question

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

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.