Question

Find the ratio in which the y axis divides the line segment joining the points (-4,-6)amd (10,12)also find the CO ordinates of the point of division

Answer 1

Answer:

Sorry I can not answer.

Answer 2

Answer:

$\bigstar{\bold{Ratio\:is\:2:5}}$

$\bigstar{\bold{Coordinates=(0,-\dfrac{6}{7}) }}$

Step-by-step explanation:

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

• Y axis divides the line segment
• Point A on line segment = (-4, -6)
• Point B on line segment = (10,12)

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Ratio in which the line is divided
• Coordinates of point of division

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

→ Let us assume the line is divided in the ratio k : 1

→ Since y axis divides the line the the coordinates at the point of division will be (0 , y)

→ By section formula,

 $(x,y)=(\dfrac{m_1x_2+m_2x_1}{m_1+m_2} ),(\dfrac{m_1y_2+m_2y_1}{m_1+m_2} )$

where m₁ = k, m₂ = 1, x₁ = -4, x₂ = 10, y₁ = -6, y₂ = 12

→ Substituting the given datas we get,

$(\dfrac{10k-4}{k+1}, \dfrac{12k-6}{k+1}) =(0,y)$

→ Equating it we get,

$\dfrac{10k-4}{k+1} =0$

10k - 4 = 0

10k = 4

k = 4/10

k = 2/5

→ Hence y axis divides the line in the ratio 2 : 5

$\boxed{\bold{Ratio\:is\:2:5}}$

→ Equating the second part

$\dfrac{12k-6}{k+1} =y$

$\dfrac{12\times \dfrac{2}{5}-6 }{\dfrac{2}{5} +1} =y$

$y=\dfrac{\dfrac{24-30}{5} }{\dfrac{7}{5} }$

y = -6/7

So the coordinate at the point of division is ( 0, -6/7)

$\boxed{\bold{Coordinates=(0,-\dfrac{6}{7}) }}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Section formula is given by

$(x,y)=(\dfrac{m_1x_2+m_2x_1}{m_1+m_2} ),(\dfrac{m_1y_2+m_2y_1}{m_1+m_2} )$