Question

If A (-14,-10), B(6,-2) is given, find the coordinates of the points which divide segment AB into four equal parts.

Answer 1

Logic Used:
1) Section Formula: 
  [tex]P(x,y)= (\frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n} ) [/tex]

where P(x,y) divides the line segment AB in the ratio m:n where 

. $A(x_{1},y_{1}) \:\: and \:\:\:B(x_{2},y_{2})$

2) Let P,Q,R divides AB into four equal parts .
We observe that P divides AB in the ratio 1:3 .
A =(-14,-10) & B =(6,-2)  

$P(x,y) = (\frac{3*-14+1*6}{3+1} , \frac{3*-10+1*-2}{3+1} ) =(-9,-8)$


3) Also, Q divides AB in the ratio 1:1 .

$Q(x,y) = (\frac{1*-14+1*6}{1+1}, \frac{1*-10+1*-2}{1+1}) =(-4,-6)$


4) And R divides AB in the ratio 3:1 .

$R(x,y)= (\frac{1*-14+3*6}{3+1}, \frac{1*-10+3*6}{3+1}) = (1,-4)$

Hence ,Required Co-ordinates are 
$\boxed{(-9,-8),(-4,-6),(1,-4)}$

Answer 2

Answer:

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