Question

Plzzz answer the question fast

Answer 1

x=x1+x2/2 y=y1+y2/2
4=2+6/2 m=3+(-3)/2
4=8/2 m=6/2
8/8=1 and 2m=6
m=6/2
m=3
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Answer 2

$\underline{\underline{\bold{\red{\: \: SOLUTION\: \:}}}}$➡

$\underline{ \bold{Given \: : }} \\ \\ \bold{Point \: \:P (4 ,\: m) \: \: divides \: \: the \: \: line \: \: segment} \\ \bold{joining \: \: the \: \: point \: \: A(2 ,\: 3) \: \: and \: \: B(6 ,\: - 3) \: .} \\ \\ \underline{\bold{To \: \: find \: : }}\: \: \: \: \: \: \: \bold{The \: \: value \: \: of \: \: m \: =?}$

$\bold{Let,} \\ \\ \bold{A(2 ,\: 3) = ( x_{1} \: ,\: y_{1}) } \\ \\ \bold{B(6 ,\: - 3) = ( x_{2} \:, \: y_{2}) } \\ \\ \bold{P(4 ,\: m) = (x ,\: y)} \\ \\ \bold{And ,\: \: the \: \: ratio \: \: \: be \: \: k : 1 \: ,\: \: which} \\ \bold{divides \: \: the \: \: line \: \: AB. \: \: } \\ \\ \bold{Now, \: } \\ \\ \bold{Using \: \:section \: \: formula \:; \: we \: \: get,} \\ \\ \bold{x = \frac{k x_{2} + 1 x_{1} }{k + 1} } \\ \\ \bold{ = > 4 = \frac{k \times 6 + 1 \times 2}{k + 1} } \\ \\ \bold{ = > 4 = \frac{6k + 2}{k + 1} } \\ \\ \bold{ = > 4k + 4 = 6k + 2} \\ \\ \bold{ = > 4k - 6k = 2 - 4} \\ \\ \bold{ = > - 2k = - 2 } \\ \\ \bold{ = > k = \frac{ - 2}{ - 2} } \\ \\ = > \bold{k = 1}$

$\bold{So, \: \: the \: \: ratio \: \: is \: \: 1 : 1 \: .}$

$\bold{Again,} \\ \\ \bold{y = \frac{k y_{2} + 1 y_{2} }{k + 1} } \\ \\ \bold{ = > m = \frac{1 \times ( - 3) + 1 \times 3}{1 + 1} } \\ \\ \bold{ = > m = \frac{ - 3 + 3}{2} } \\ \\ = > \bold{m = \frac{0}{2} } \\ \\ = > \bold{m = 0}$

$\bold{Hence \: \: \:the \: \: value \: \: of \: \: m = 0 }$

$\underline{\underline{\bold{\red{\: \: ANSWER\: \:}}}}$➡ $\boxed{\boxed{\huge{\bold{\purple{\: \: m = 0 \: \:}}}}}$

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✝$\mathfrak{\red{THANKS..}}$✝