Find the ratio in which the line segment joining the points (3.-5) and

1.	Find the ratio in which the line segment joining the points (3.-5) and(-4, 2) is divided by the y-axis. Also find the coordinates of the point of division
Answer» Answer: $\bigstar{\bold{Ratio=3:<klux>4</klux>}}$ $\bigstar{\bold{Coordinates=(0,-2)}}$ Step-by-step explanation: $\Large{\underline{\rm{Given:}}}$ Point A (3, -5) Point B (-4,2) $\Large{\underline{\rm{To\:Find:}}}$ Ratio in which the line segment is divided by they y axis Coordinates of the point of division $\Large{\underline{\rm{Solution:}}}$ ➛ Here we have to first find the ratio in which the line segment is divided. ➛ LET us assume it is divided in the ratio K : 1. ➛ By section formula, $\tt (x,y)=\bigg(\dfrac{m_1x_2+m_2x_1}{m_1+m_2} ,\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\bigg)$ ➛ Here given that the line segment is divided by the y axis. ➛ Hence the coordinates of point of division are (0, y). Here x = 0, y = y, m₁ = k, m₂ = 1, x₁ = 3, x₂ = -4, y₁ = -5, y₂ = 2 ➛ SUBSTITUTING the datas we get, $\tt (0,y)=\bigg(\dfrac{-4k+3}{k+1} ,\dfrac{2k-5}{k+1} \bigg)$ ➛ Equating the x coordinate we get, $\tt \dfrac{-4k + 3}{k+1}=0$ ➛ Cross multiplying, -4k + 3 = 0 -4k = -3 k = 3/4 ➛ Hence the line segment is divided in the ratio 3 : 4. $\boxed{\bold{Ratio=3:4}}$ ➛ Now FINDING the coordinates of point of division, ➛ Equating the y coordinate, $\tt \dfrac{2k-5}{k+1} =y$ ➛ Substitute the value of k and cross multiply, 2 × 3/4 - 5 = y ( 3/4 + 1) 6/4 - 5 = 7/4 × y (6 - 20)/4 = 7/4 × y 7y = - 14 y = -2 ➛ Hence the coordinates of point of division are (0, -2). $\boxed{\bold{Coordinates=(0,-2)}}$