Question

find the ratio in which the line segment joining the points (2,3) and (-4,5) is divided by the y axis also find the coordinates of the point of division​

Answer 1

Answer:

1 : 2 ; ( 0 , $\frac{11}{3}$ )

Step-by-step explanation:

If a point ( x , y ) divides the line segment joining the points ( $x_{1}$ , $y_{1}$ ) and ( $x_{2}$ , $y_{2}$ ) in the ratio m : n , then ( x , y ) = ( $\frac{mx_{2} +nx_{1} }{m+n}$ , $\frac{my_{2} +ny_{1} }{m+n}$ )

~~~~~~~~~~~~

( 2 , 3 )

( - 4 , 5 )

( x , y ) = ( $\frac{-4m+2n}{m + n}$ , $\frac{5m+3n}{m+n}$ ) , as the point lies on y-axis, x-coordinates equals to 0 ⇒ $\frac{-4m+2n}{m + n}$ = 0 ⇒ - 4m + 2n = 0

4m = 2n ⇒ m : n = 1 : 2

( 0 , $\frac{5+6}{3}$ ) = ( 0 , $\frac{11}{3}$ )

Answer 2

Answer:

1 : 2 ; ( 0 , )

Step-by-step explanation:

If a point ( x , y ) divides the line segment joining the points ( , ) and ( , ) in the ratio m : n , then ( x , y ) = ( , )

~~~~~~~~~~~~

( 2 , 3 )

( - 4 , 5 )

( x , y ) = ( , ) , as the point lies on y-axis, x-coordinates equals to 0 ⇒ = 0 ⇒ - 4m + 2n = 0

4m = 2n ⇒ m : n = 1 : 2

( 0 , ) = ( 0 , )