Question

Find the co-ordinates of point P joining the line segment (8, -9) and (2, 3) in ratio 1:2 internally.​

Answer 1

Answer:

Explanation:

Given :

• Point P joining the line segment (8, -9) and (2, 3) in ratio 1:2 internally.

To Find :

• The co-ordinate of point P.

Solution :

Let,

• A(8 , -9) = (x₁ , y₁)
• B(2 , 3) = (x₂ , y₂)
• m : n = 1 : 2

Applying section formula,

$\tt \red{ x = \dfrac{mx_2 + nx_1}{m + n} \: \: \: \: \green{and} \: \: \: \: \: \: \: y = \dfrac{my_2 + ny_1}{m + n} }$

Now,

$: \implies \tt \: x = \dfrac{1 \times 2 + 2 \times 8}{1 + 2} \: \: \: \: \: \: \: and \: \: \: \: \: \: y = \dfrac{1 \times 3 + 2 \times ( - 9)}{1 + 2} \\ \\ \\ : \implies \tt \: x = \dfrac{2 + 16}{3} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: y = \dfrac{3 - 18}{3} \\ \\ \\ : \implies \tt \: x = \dfrac{18}{3} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: y = \dfrac{ - 15}{3} \\ \\ \\ : \implies \tt \: x = \not\dfrac{18}{3} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: y = \not\dfrac{ - 15}{3} \\ \\ \\ : \implies \tt \red{ x = 6} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \green{y = - 5} \\ \\ \\ : \implies \tt \purple{ \therefore \: p(x,y) = (6, - 5)} \\ \\ \\ \underline{ \therefore \tt \: The \: co - ordinate \: of \: point \: P \: is \: (6,- 5).}$

Answer 2

$\huge\mathfrak{\underline{\color{purple}{{{Solution :}}}}}$

Let,

• A(8 , -9) = (x₁ , y₁)

• B(2 , 3) = (x₂ , y₂)

• m : n = 1 : 2

$\sf{ \color{teal}{Applying~ section ~formula,}}$

$\boxed{\bf {\purple{{ x = \dfrac{mx_2 + nx_1}{m + n} \: \: \: \: and\: \: \: \: \: \: \: y = \dfrac{my_2 + ny_1}{m + n} }}}}$

Now,

$\begin{gathered}\implies \rm \:{ \orange{ x = \dfrac{1 \times 2 + 2 \times 8}{1 + 2} \: \: \: \: \: \: \: and \: \: \: \: \: \: y = \dfrac{1 \times 3 + 2 \times ( - 9)}{1 + 2} }}\\ \\ \\ \implies \rm\: { \orange{x = \dfrac{2 + 16}{3} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: y = \dfrac{3 - 18}{3}}} \\ \\ \\ \implies \rm\: { \orange{x = \dfrac{18}{3} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: y = \dfrac{ - 15}{3} }}\\ \\ \\ \implies \rm\: { \orange{x = \cancel\dfrac{18}{3} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: y = \cancel\dfrac{ - 15}{3}}} \\ \\ \\ \implies \rm {\underline{\pink{{x = 6 \: \: \: \: \: \: \: and \: \: \: \: \: \: \: {y = - 5}}}}} \\ \\ \\ \boxed{ \implies \rm \red{ \therefore \: p(x,y) = (6, - 5)}} \\ \\ \\ \underline{ \therefore \sf{ \color{green}{The \: co - ordinate \: of \: point \: P \: is \: (6,- 5).}}}\end{gathered}$