Question

A=(2,3),B=(8,9) and C=(x,y) divides AB in the ratio 1:5 internally, then C=​

Answer 1

Answer:

x = 5(2) + 1(8) / 1+5                y = 5(3) + 1(9) / 1+5

x = 10+8/6                              y = 15+9/6

x = 18/6                                  y = 24/6

x = 3                                       y = 4

so, the coordinate of c =(3,4)

Answer 2

The coordinates of C = (3, 4)

Given:

The points A(2,3) and B(8,9) are forms AB  

And C(x,y) divides AB in the ratio 1:5 internally.

To find:

The coordinates of C(x, y)

Solution:

If the points A and B are (x₁, y₁) and (x₂, y₂) respectively and c(x, y) divides AB in m:n ratio then Internal Section Formula is given by

C(x, y) = $( \frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n} )$  

From given data A (2,3), B (8,9) and C (x, y) and m : n = 1 : 5

⇒ C (x, y) = $( \frac{(1)(8)+(5)(2)}{1+5} , \frac{(1)(9)+(5)(3)}{1+5} )$  

⇒ C (x, y) = $( \frac{8+10}{6} , \frac{9+15}{6} )$

⇒ C (x, y) =  $( \frac{18}{6} , \frac{24}{6} )$  

⇒ C (x, y) =  (3, 4)

Therefore, the coordinates of C = (3, 4)

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