Question

. Write the ratio in which the line segment joining points (2, 3) and (3,-2) is divided by X axis.​

Answer 1

$\tt \blue{ Let:- }$

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$\blue \bullet \footnotesize\tt { \: \: Ratio \: = \: k:1 }$

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$\bullet\tt \blue{ \:Solution:- }$

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$\blue \bullet \footnotesize\tt { \: M1 = k }$

$\blue \bullet \footnotesize\tt { \: M1 = 2 }$

$\blue \bullet \footnotesize\tt { \: y = 0 }$

$\blue \bullet \footnotesize\tt { \: y1 = 3 }$

$\blue \bullet \footnotesize\tt { \: y2 = -2 }$

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$\bullet\tt \blue{\: Using \: Section \: formula }$

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$\blue \mapsto \footnotesize \tt{ y } \tt{ \: = \frac{m1y2 \: - \: m2y1}{m1 \: + \: m2} }$

$\blue \mapsto \footnotesize \tt{ 0} \tt{ \: = \frac{k( - 2) \: + \: 1(3)}{k \: + \: 1} }$

$\blue \mapsto\footnotesize \tt{ 0 } \tt{ \: = \frac{ - 2k\: + \: 3}{k \: + \: 1} }$

$\blue \mapsto\footnotesize\tt{ 0 ( k + 1)= - 2k\: + 3}$

$\blue \mapsto\footnotesize\tt{ 0 = - 2k\: + 3}$

$\blue \mapsto \footnotesize\tt{ 0 - 3 = - 2k\: }$

$\blue \mapsto\footnotesize\tt{ - 3= - 2k\: }$

$\blue \mapsto \footnotesize\tt{ \cancel- 3= \cancel - 2k\: }$

$\blue \mapsto\footnotesize\tt{ 3= 2k}$

$\blue \mapsto\boxed{ \boxed{ \underline{\underline{\footnotesize\tt{ \blue \bullet \: k = \frac{3}{2} }}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mapsto\tt \blue{ Ratio = 3:2 }$