Question

If the point C (x, 3) divides the line joining points 4(2, 6) and B(5, 2) in the ratio 2: 1 then the value of x is

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Answer 1

Solution :-

we know that, when a point P(x, y) divides the line joining the points A(x1,y1) and B(x2, y2) in the ratio m : n , then :-

• x = (mx2 + nx1)/(m + n)

given that,

• A(x1,y1) = A(2,6)
• B(x2,y2) = B(5,2)
• m : n = 2 : 1

so, putting all values we get,

→ x = (mx2 + nx1)/(m + n)

→ x = (2 * 5 + 1 * 2)/(2 + 1)

→ x = (10 + 2)/3

→ x = (12/3)

→ x = 4 (Ans.)

Hence, value of x is equal to 4 .

Also, checking for y coordinate ,

→ y = (my2 + ny1)/(m + n)

→ y = (2 * 2 + 1 * 6)/(2 + 1)

→ y = (4 + 6)/3

→ y = 10/3

but since it is given that, y coordinate of point P is 3 , therefore given data is incorrect .

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Answer 2

★given:-

• point C (x, 3) divides the line joining points 4(2, 6) and B(5, 2) in the ratio 2: 1

★find:-

• value of x

★SOLUTION:-

• we know that line joining x point formula who divide ratio

$\implies \star\pink{x = \frac{ m_{1} x_{2} + m_{1} x_{1} }{ m_{1} + m_{2} } }$

where

$\implies \: x_{1} = 2 \\ \\ \implies \: x_{2} = 5 \\ \\ \implies \: m_{1} = 2 \\ \\ \implies \: m_{2} = 1$

put value on formula

$\implies \: x = \frac{(2)(5) + (1)(2)}{2 + 1} \\ \\ \implies \: x = \frac{10 + 2}{3} \\ \\ \implies \: x = \frac{ \: \cancel{12}}{ \cancel{3}} \\ \\ \implies \boxed{x = 4}$

value of x

$\boxed{ \red{x = 4}}$

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I hope it helps you