Question

find the cordinates of the point which divides intenally the line joining the point 6,-9 and 4,6 in the ratio 3:4​

Answer 1

Given :

• Points (6,-9) and (4,6)

To Find :

• Cooridinates of the point which divides them in the ratio 3:4 .

Solution :

$\longmapsto\tt{{x}_{1}=6}$

$\longmapsto\tt{{x}_{2}=4}$

$\longmapsto\tt{{y}_{1}=-9}$

$\longmapsto\tt{{y}_{2}=6}$

For x :

Using Section Formula :

$\longmapsto\tt\boxed{x=\dfrac{{m}_{1}{x}_{2}+{m}_{2}{x}_{1}}{{m}_{1}+{m}_{2}}}$

Putting Values :

$\longmapsto\tt{x=\dfrac{3\times{4}+4\times{6}}{3+4}}$

$\longmapsto\tt{x=\dfrac{12+24}{7}}$

$\longmapsto\tt\bf{x=\dfrac{36}{7}}$

Similarly :

For y :

Using Section Formula :

$\longmapsto\tt\boxed{y=\dfrac{{m}_{1}{y}_{2}+{m}_{2}{y}_{1}}{{m}_{1}+{m}_{2}}}$

Putting Values :

$\longmapsto\tt{y=\dfrac{3\times{6}+4\times{(-9)}}{3+4}}$

$\longmapsto\tt{y=\dfrac{12-36}{7}}$

$\longmapsto\tt\bf{y=\dfrac{-18}{7}}$

So , The Cooridinates of the point is 36/7 and -18/7 .

Answer 2

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• $\tiny\boxed{\sf{\purple{Coordinates\:of\:the\:point\:=\:\bigg(\dfrac{36}{7}\:,\:\dfrac{-18}{7}\bigg)}}}$

Explanation :

$\underline{\underline{\bf{Given\::-}}}$

• A point divides the line segment joining points (6 , -9) and (4 , 6) in the ratio 3:4.

$\underline{\underline{\bf{To\:Find\::-}}}$

• Coordinates of the point ?

$\underline{\underline{\bf{Solution\::-}}}$

★ Using section formula :-

$\small\longrightarrow\:\sf Coordinates\:=\:\bigg(\dfrac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}}\:,\:\dfrac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}\bigg)$

Where,

• $\sf m_{1} = 3\:,\:m_{2} = 4$
• $\sf x_{1} = 6\:,\:x_{2} = 4$
• $\sf y_{1} = -9\:,\:y_{2} = 6$

★ Putting all known values :-

$\small\longrightarrow\:\sf Coordinates\:=\:\bigg(\dfrac{(3\:\times\:4) + (4\:\times\:6)}{3 + 4}\:,\:\dfrac{(3\:\times\:6) + [4\:\times\:(-9)]}{3 + 4}\bigg)$

$\small\longrightarrow\:\sf Coordinates\:=\:\bigg(\dfrac{12 + 24}{7}\:,\:\dfrac{18 + (-36)}{7}\bigg)$

$\small\longrightarrow\:\sf Coordinates\:=\:\bigg(\dfrac{36}{7}\:,\:\dfrac{18 - 36}{7}\bigg)$

$\small\longrightarrow\:\underline{\underline{\sf {Coordinates\:=\:\bigg(\dfrac{36}{7}\:,\:\dfrac{-18}{7}\bigg)}}}$

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$\underline{\underline{\bf{More\:to\:know\::-}}}$

• For finding distance b/w two points, we use distance formula, i.e, $\sf \sqrt{\bigg(x_{2} - x_{1}\bigg)^2 + \bigg(y_{2} - y_{1}\bigg)^2}$

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