Question

find the ratio in which the line segment joining the points (-7,5) and (-2,-5) is divided by (-4,-1) answer ​

Answer 1

Answer:

$\bigstar{\bold{Ratio=3:2}}$

Step-by-step explanation:

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

• Point A = (-7, 5)
• Point B = (-2, -5)
• Point C = (-4, -1)

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

• To find the ratio in which Point C divides the line segment joining the points A and B

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

→ Let us assume the ratio as k : 1

→ By section formula we know that,

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

  where x = -4, y = -1, x₁ = -7, x₂ = -2, y₁ = 5, y₂ = -5,m₁ = k, m₂ = 1

→ Substitute the data,

  $\sf{(-4,-1) = \bigg(\dfrac{-2k-7}{k+1} ,\dfrac{-5k+5}{k+1}\bigg)}$

→ Equating it we get,

  (-2k - 7)/(k + 1) = -4

   -2k - 7 = -4(k + 1)

   -2k - 7 = -4k -4

   -2k + 4k = -4 + 7

    2k = 3

      k = 3/2

→ Now equating the y coordinate,

   (-5k + 5)/(k + 1) = -1

    -5k + 5 = -k - 1

    -5k + k = -1 - 5

    -4k = -6

       k = 6/4

       k = 3/2

→ Hence the line is divided in the ratio 3 : 2

$\boxed{\bold{Ratio=3:2}}$

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

→ The section formula is given by,

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