Question

y find the cooridnate of the points which divide the line segment joining the point p(4,3)&q(9,7) in the ratio 3:2​

Answer 1

Given:-

• Two points P(4, 3) and Q(9, 7) are such that when we join them a line segment us formed.
• Ratio in which the line segment divides = 3:2

To Find:-

• Coordinates of the point that divides this line segment.

Assumption:-

• Let the coordinates of the points dividing the line segment be A(x, y)

Solution:-

We have:-

• P(4, 3)
• Q(9, 7)
• Ratio = 3:2

We already know:-

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

From given we have:-

• x₁ = 4
• x₂ = 9
• y₁ = 3
• y₂ = 7
• m₁ = 3
• m₂ = 2

Putting all the values in the formula:-

$= \tt{A(x, y) = \bigg(\dfrac{3 \times 9 + 2 \times 4}{3 + 2}, \dfrac{3 \times 7 + 2 \times 3}{3 + 2}\bigg)}$

$= \tt{A(x, y) = \bigg(\dfrac{27 + 8}{5}, \dfrac{21 + 6}{5}\bigg)}$

$= \tt{A(x, y) = \bigg(\dfrac{35}{5}, \dfrac{27}{5}\bigg)}$

$= \tt{A(x, y) = (7, 5.4)}$

∴ The coordinates of the points that divides P(4, 3) and Q(9, 7) in the ratio 3:2 is (7, 5.4).

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More Information!!

• x₁ is the abscissa of the first point
• x₂ is the abscissa of the second point
• y₁ is the ordinate of the first point
• y₂ is the ordinate of the second point
• m₁ is the antecedent of the ratio
• m₂ is the consequent of the ratio

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