Question

Find the coordinates of the point which divides A(4, −3) and B(8,5) externally

in the ratio 3:1.​

Answer 1

Given :

• Coordinates of A = ( 4 , - 3 )

• Coordinates of B = ( 8 , 5 )

• Ratio ( m₁ : m₂ ) = 3 : 1

To Find :

• Coordinates of point which divides line in 3 : 1 part

Solution :

By using section formula

$\large \implies \boxed{ \boxed{\sf x = \frac{m_1x_2 +m_2x_1 }{m_1 + m_2}}} \\ \\ \sf \implies x = \frac{3 \times 8 + 1 \times4}{3 + 1} \\ \\\sf \implies x = \frac{24 + 4}{4} \\ \\ \sf \implies x = \frac{28}{4} \\ \\ \large \implies \boxed{ \sf x =4}$

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$\large \implies \boxed{ \boxed{\sf y = \frac{m_1y_2 +m_2y_1 }{m_1 + m_2}}} \\ \\\sf \implies y = \frac{3 \times 5 + 1 \times ( - 3)}{3 + 1} \\ \\\sf \implies y = \frac{15 - 3}{4} \\ \\\sf \implies y = \frac{12}{4} \\ \\ \large\implies \boxed{ \sf y = 3}$

Coordinates of point = ( 4 , 3 )

Answer 2

Refer to the attachment ☺️