Question

Find the ratio in which the point ( -3 , k ) divides the line segment joining the points ( -5, -4 ) and ( -2, 3 ), Also find the value of k.

Answer 1

hope this will help u

Answer 2

$\tiny{\mathsf{SOLUTION;-}}$

$\tiny{\mathsf{Given;-}}$

$\implies\tiny{ \mathsf{let \: p( - 3, \: k) \: divide \: ab \: in \: the \: ratio \: \: (a \ratio1)}} \\ \\ \\ \implies\tiny{ \mathsf{now \: by \: using \: section \: formula \: the \: coordinates \: of \: p \: are}} \\ \\ \\ \implies \tiny{ \mathsf{p( \frac{ - 2a - 5}{a + 1} \:, \frac{3a - 4}{a + 1}}}) \\ \\ \\ \implies \tiny{ \mathsf{using \: p( - 3, \: k)}} \\ \\ \\ \implies \tiny{ \mathsf{ \frac{ - 2a - 5}{a + 1} = - 3 \: \: and \: \: \frac{3a - 4}{a + 1} = k}} \\ \\ \implies \tiny{ \mathsf{ - 2a - 5 = - 3a - 3}} \\ \\ \implies \tiny{ \mathsf{ - 2a + 3a = - 3 + 5}} \\ \\ \implies \tiny{ \mathsf{a = 2}} \\ \\ \implies { \fbox{\tiny{ \mathsf{hence \: the \: required \: ratio \: is \: 2 \ratio1}}}} \\ \\ \\ \implies \: \tiny{ \mathsf{putting, \: a= 2}} \\ \\ \implies \tiny{ \mathsf{\frac{3(a) - 4}{(a) + 1} = k}} \\ \\ \\\implies \tiny{ \mathsf{\frac{3(2) - 4}{(2) + 1} = k}} \\ \\ \implies \tiny{ \mathsf{ \frac{6 - 4}{3} = k}} \\ \\ \implies \tiny{ \mathsf{k = \frac{2}{3}}} \\ \\ \\ \implies \tiny{ \mathsf{ \fbox{ \: hence ,\: k = \frac{2}{3}}}}$