Question

9) If point P divides segment AB in the ratio 1:3 where A(-5 , 3) and

B(3 , -5) then the coordinates of P are -----------------

A)( -2, -2 ) B)( -1 , -1 ) C) (-3 , 1 ) D) ( 1, - 3 )​

Answer 1

Given: Given that, point P divides the line segment AB in the ratio of 1:3 where,

• A(-5,3)
• B(3,-5)

To find: We need to find the coordinates of P.

Solution: From the given: A(-5,3) and B(3,-5), we know that:

• $\sf{x_1 = -5}$
• $\sf{x_2 = 3}$
• $\sf{y_1 = 3}$
• $\sf{y_2 = -5}$

We know that Point P divides the line segnent in the ratio 1:3. So, let:

• $\sf{m_1 = 1}$
• $\sf{m_2 = 3}$

In this problem, we are going to use the section formula. We know that,

$\begin{gathered}\begin{gathered}\\\longrightarrow\bf{P = \dfrac{m_1x_2+m_2x_1}{m_1+m_2} , \dfrac{m_1y_2+m_2y_1}{m_1+m_2}}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\\longrightarrow\bf{P = \dfrac{1 \times 3+3 \times (-5)}{1+3} , \dfrac{1 \times (-5)+ 3 \times 3}{1+3}}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\\longrightarrow\bf{P = \dfrac{3-15}{4} , \dfrac{-5+9}{4}}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\\longrightarrow\bf{P = \dfrac{-12}{4} , \dfrac{4}{4}}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\\longrightarrow{\boxed{\green{\frak{P = (-3,1)}}}}\end{gathered}\end{gathered}$

Hence, the coordinates of P is (-3,1).

Our correct option is C.