Question

In what ratio is the line segment joining the points (-2,3) and (3,7) divided by the y-axis.Also find the coordinates of the point of division​

Answer 1

SOLUTION:-

•Let the y-axis cut the join of A (-2,-3) and B(3,7) at point P in the ratio

k:1

$\bf \color{aqua}{➣Then \: by \: section \: formula \: the \: coordinates \: of \: P \: are :}$

$\bf \purple{\: p {\bigg (} \frac{3k - 2}{k + 1} , \frac{7k - 3}{k + 1} { \bigg)}}$

$\textsf{but p lies on the y axis .so its abscissa is 0}$

$\bf \green{ \therefore \frac{3k - 2}{k + 1} = 0} \implies \red{3k - 2 = 0} \implies \pink{k = \frac{2}{3} }$

•So,the required ratio is

$\bf{ \color{yellow} \frac{2}{3}:1} \implies \: which \: is \: \orange{2 : 3}$

$\bf putting \:{ \color{aqua}{ \boxed{ \bf \: k = \: \frac{2}{3} }} } \: we \: get \: the \: point \: p \: as$

$\bf \: \green{ \: p{ \bigg \{ }0, \: \frac{7 \times \frac{2}{3} - 3 } { \frac{2}{3} + 1 } { \bigg \}}}$

$\bf \purple{ i.e \: p(0,1) }$

•Hence ,the point of intersection of AB and the y axis is P(0,1)