Question

Find the coordinates of the point which divides the line joining the points (– 1, 7) and (4 ,– 3)

Internally in the ratio 2:3​

Answer 1

Answer:-

Given:

A point divides the line segment joining the points ( - 1 , 7) & (4 , - 3) internally in the ratio 2 : 3.

Using section formula;

i.e., The co - ordinates of a point which divides the line segment joining the points (x₁ , y₁) & (x₂ , y₂) internally in the ratio m : n are :

(x , y) = [ mx₂ + nx₁ / m + n , my₂ + ny₁ / m + n ]

Let,

• x₁ = - 1

• x₂ = 4

• y₁ = 7

• y₂ = - 3

• m = 2

• n = 3

Hence,

⟶ ( x , y ) = [ { (2)(4) + (3)( - 1) }/ 2 + 3 , { (2)(- 3) + (3)(7) } / 2 + 3 ]

⟶ (x , y) = [ (8 - 3)/5 , (- 6 + 21)/5 ]

⟶ (x , y) = [ 5/5 , 15/5 ]

⟶ (x , y) = (1 , 3)

Therefore, the co - ordinates of the point are (1 , 3).

Answer 2

Answer:

To solve our given problem we will use section formula :]

• Section Formula states that, when a point divides a line segment internally in the ratio m:n, So the coordinates are :]

$\tiny: \implies (x,y) = \bigg \lgroup x = \frac{m. {x}_{2} +n. {x}_{1} }{m + n} ,y= \frac{m. {y}_{2} +n. {y}_{1} }{m + n} \bigg \rgroup$

Let

• (-1 , 7) = (x₁ , y₁)

• (4 , -3) = (x₂ , y₂)

• m = 2

• n = 3

Upon Substituting coordinates of our given points in section Formula we get :]

$\tiny: \implies (x,y) = \bigg \lgroup x = \frac{2 \times 4 +3 \times - 1 }{2 + 3} ,y= \frac{2 \times - 3 +3 \times 7}{2 + 3} \bigg \rgroup$

$\tiny: \implies (x,y) = \bigg \lgroup x = \frac{8 - 3 }{2 + 3} ,y= \frac{ - 6 +21}{2 + 3} \bigg \rgroup$

$\tiny: \implies (x,y) = \bigg \lgroup x = \frac{5 }{5} ,y= \frac{15}{5} \bigg \rgroup$

$\tiny: \implies (x,y) = \bigg \lgroup x = 1,y= 3 \bigg \rgroup$