Question

The point which divides A(0, 1) and B(3, -1) externally in the ratio 3 : 1 is

Answer 1

Answer:

(x, y) = (9/2, -2)

Step-by-step explanation:

if External ratio = 3:1

then internal ratio = -3:1

Let the point of division be (x, y)

(x, y) = {(-3*3 + 1*0)/(-3+1) , (-3*(-1)+1*1)/(-3+1)}

x = -9/-2 = 9/2

y = 4/-2 = -2

(x, y) = (9/2, -2)

Answer 2

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

$\begin{gathered}\large \implies \boxed{ \boxed{\sf x = \frac{m_1x_2 +m_2x_1 }{m_1 + m_2}}} \\ \\ \sf \implies x = \frac{3 \times 8 + 1 \times4}{3 + 1} \\ \\\sf \implies x = \frac{24 + 4}{4} \\ \\ \sf \implies x = \frac{28}{4} \\ \\ \large \implies \boxed{ \sf x =4}\end{gathered} </p><p>$

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$\begin{gathered}\large \implies \boxed{ \boxed{\sf y = \frac{m_1y_2 +m_2y_1 }{m_1 + m_2}}} \\ \\\sf \implies y = \frac{3 \times 5 + 1 \times ( - 3)}{3 + 1} \\ \\\sf \implies y = \frac{15 - 3}{4} \\ \\\sf \implies y = \frac{12}{4} \\ \\ \large\implies \boxed{ \sf y = 3}\end{gathered} </p><p>$

Coordinates of point = ( 4 , 3 )