20. Find the co-ordinates of
the point which divides the join
(4,-5) &(6,3) in the ratio 3:5​

1 thought on “20. Find the co-ordinates of<br />the point which divides the join<br />(4,-5) &(6,3) in the ratio 3:5​”

1. Given:-

   Points:-

   • (4, -5)
   • (6, 3)

   • Ratio = 3:5

   To Find:-

   • The co-ordinates of the point which divides the line joining (4, -5) and (6, 3) in the ratio 3:5

   Assumption:-

   • Let the point dividing the line segment be P(x, y)

   Solution:-

   We have:-

   • x₁ = 4
   • x₂ = 6
   • y₁ = -5
   • y₂ = 3
   • m₁ = 3 (antecedent of the ratio)
   • m₂ = 5 (consequent of the ratio)

   We already know:-

   • [tex]\dag{\boxed{\underline{\tt{Section\:Formula =\bigg( \dfrac{m_1 x_2 + m_2 x_1}{m_1 + m_2}, \dfrac{m_1 y_2 + m_2 y_1}{m_1 + m_2}\bigg)}}}}[/tex]

   Putting all the values in the formula:-

   [tex]\sf{P(x, y) = \bigg(\dfrac{3 \times 6 + 5 \times 4}{3 + 5}, \dfrac{3 \times 3 + 5 \times (-5)}{3 + 5}\bigg)}[/tex]

   [tex] = \sf{P(x, y) = \bigg(\dfrac{18 + 20}{8}, \dfrac{9 – 25}{8}\bigg)}[/tex]

   [tex] = \sf{P(x, y) = \bigg(\dfrac{38}{8}, \dfrac{16}{8}\bigg)}[/tex]

   [tex] = \sf{P(x, y) = \dfrac{\not{38}}{\not{8}}, \dfrac{\not{16}}{\not{8}}}[/tex]

   [tex] = \sf{P(x, y) = \dfrac{19}{4}, 2}[/tex]

   ∴ The coordinates of the point that divides the line segment joining (4, –5) and (6, 3) in the ratio 3:5 are (19/4, 2).

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   Remember!!!!

   • x₁ = abscissa of the first point
   • x₂ = abscissa of the second point
   • y₁ = ordinate of the first point
   • y₂ = ordinate of the second point
   • m₁ = antecedent of the ratio (i.e. 3:5)
   • m₂ = consequent of the ratio (i.e 3:5)

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