Question

if C divides the line AB in 1:2 ratio then find the coordonate of C.where coordinate of A and B are (5,8) and (1,-3) respectively​

Answer 1

Answer :

The coordinates of point C -  $\bf (\frac{11}{3},\frac{13}{3})$

Step-by-step explanation :

Let the coordinates of C be (x , y)

It divides the line AB on the ratio 1 : 2

So, let m = 1 , n = 2

The coordinates of points A and B are (5 , 8) and (1 , -3) respectively.

Let A (5 , 8) = (x₁ , y₁)

     B (1 , -3) = (x₂ , y₂)

• x₁ = 5
• x₂ = 1
• y₁ = 8
• y₂ = -3

If a point of coordinates (x , y) divides the line joining the two points (x₁ , y₁) and (x₂ , y₂) in the ratio m : n , then

  $\implies \sf x=\frac{mx_2+nx_1}{m+n} \\\\ \implies y=\frac{my_2+ny_1}{m+n}$

Substituting the values,

x - coordinate is :

     $\sf x=\frac{1(1)+2(5)}{1+2} \\\\ x=\frac{1+10}{3} \\\\ x=\frac{11}{3}$

y - coordinate is :

    $\sf y=\frac{1(-3)+2(8)}{1+2} \\\\ y=\frac{-3+16}{3} \\\\ y=\frac{13}{3}$

The coordinates of the point C is  $\bf (\frac{11}{3},\frac{13}{3})$