Question

find the co-ordinates of Arout point p if p divided
the line segment joining the points A (-1,1)
and B(4,-3) in the ratto 2:3​

Answer 1

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

$\sf \implies Coordinates \: of \: point \: A = (-1, 1)$

$\sf \implies Coordinates \: of \: point \: B = (4, - 3)$

$\sf \implies Ratio \: in \: which \: P \: divides \: A \: and \: B \: is \: 2 : 3$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies Coordinates \: of \: point \:  P = \: ?$

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

$\bf \underline{ Using\;section\;formula} :$

$\underline{{\boxed{\sf{P(x,y) = \bigg( \dfrac{m_2 x_1 + m_1 x_2}{m_1 + m_2}\;,\; \dfrac{m_2 y_1 + m_1 y_2}{m_1 + m_2} \bigg)}}}}$

$\bf \underline{Where},$

$\sf \implies m_1 = 2$

$\sf \implies m_2= 3$

$\sf \implies x_1 = - 1$

$\sf \implies x_2= 4$

$\sf \implies y_1 = 1$

$\sf \implies y_2= - 3$

$\sf \underline{Substituting \: the \: values},$

$\sf{P(x,y) = \bigg( \dfrac{m_2 x_1 + m_1 x_2}{m_1 + m_2}\;,\; \dfrac{m_2 y_1 + m_1 y_2}{m_1 + m_2} \bigg)}$

$\bf \underline{Now},$

$\sf{P(x,y) = \bigg( \dfrac{3 \times (- 1) + 2 \times 4}{2 + 3}\;,\; \dfrac{3 \times 1 + 2 \times ( - 3)}{2 + 3} \bigg)}$

$\sf{P(x,y) = \bigg( \dfrac{ - 3 + 8}{5}\;,\; \dfrac{3 + ( - 6)}{5} \bigg)}$

$\sf{P(x,y) = \bigg( \cancel{ \dfrac{ 5}{5}}\;,\; \dfrac{3 - 6}{5} \bigg)}$

$\sf{P(x,y) = \bigg( 1\;,\; \dfrac{ - 3}{5} \bigg)}$

$\underline{\boxed{\bf \red{Hence , the \: required\:coordinates \: of \: the \: point\:are \bigg( 1 \:,\:\dfrac{ - 3}{5}\bigg)}}}$