Question

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

Answer 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:-

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

Putting all the values in the formula:-

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

$= \sf{P(x, y) = \bigg(\dfrac{18 + 20}{8}, \dfrac{9 - 25}{8}\bigg)}$

$= \sf{P(x, y) = \bigg(\dfrac{38}{8}, \dfrac{16}{8}\bigg)}$

$= \sf{P(x, y) = \dfrac{\not{38}}{\not{8}}, \dfrac{\not{16}}{\not{8}}}$

$= \sf{P(x, y) = \dfrac{19}{4}, 2}$

∴ 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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