Question

find the coordinates of the point which divides the line segment joining the two points (4,-3) and (8,5) are in the ratio 3:1​

Answer 1

Given: We're given with, two points (4, –3) & (8, 5) are in the ratio of 3: 1.

Topic : Co – ordinate Geometry.

Need to find: We've to find out the co – ordinates.

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❍ Let's say, that the point x(x, y) is the point which divides the line segment.

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¤ To find out the co – ordinates, we'll use the Section formula which is given by —

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$\bigstar\:\underline{\boxed{\sf{\Big\{x, y\Big\} = \bigg\{\dfrac{m_1 x_2 + n_2 x_1}{m + n}, \;\dfrac{m_1 y_2 + m_2 y_1}{m + n}\bigg\}}}}$

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$\dashrightarrow\sf \Bigg\{\dfrac{3\Big\{8\Big\} + 1\Big\{4\Big\}}{3 + 1}, \dfrac{3\Big\{5\Big\} + 1\Big\{-3\Big\}}{3 + 1}\Bigg\} \\\\\\\dashrightarrow\sf \dfrac{24 + 4}{3 + 1}, \dfrac{15 + (-3)}{3 + 1} \\\\\\\dashrightarrow\sf \cancel\dfrac{28}{4}, \: \cancel\dfrac{12}{4} \\\\\\\dashrightarrow\underline{\boxed{\pmb{\frak{7, 3}}}}\;\bigstar$

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$\therefore{\underline{\textsf{Hence, \textbf{(7, 3)} is the point which divides the line segment internally.}}}$

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$\qquad\quad\underline{\bigstar\:{\pmb{\mathbb{ADDITIONAL~ INFORMATION \: \: }} }}$

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• To calculate the distance b/w two given points (x₁, x₂) and (y₁, y₂) the distance formula is given by :$\sf{\sqrt{\bigg(x_2 - x_1 \bigg)^2 + \bigg(y_2 - y_1 \bigg)^2}}$⠀

Answer 2

Given :-

Point  (4,-3) and (8,5) are in the ratio 3:1​

To Find :-

Coordinate

Solution :-

We know that

$\sf (x,y) = \bigg(\dfrac{mx_2 + nx_1}{m + n},\dfrac{my_2+my_1}{m+n}\bigg)$

So,

Here

m:n = 3:1

m = 3

n = 1

On putting values

$\sf (x,y) = \bigg(\dfrac{3 \times8 + 1\times 4}{3+1} , \dfrac{3\times5 + 1\times -3}{3 + 1}\bigg)$

$\sf (x,y) = \bigg( \dfrac{24 + 4}{4}, \dfrac{15 + -3}{4}\bigg)$

$\sf (x,y) = \bigg(7,\dfrac{12}{4}\bigg)$

$\sf (x,y) = (7,3)$