Question

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 1

Answer:

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Answer 2

Answer:

$\bigstar{\bold{Ratio=3:4}}$

$\bigstar{\bold{Coordinates=(0,-2)}}$

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).

    $\boxed{\bold{Coordinates=(0,-2)}}$