Question

If A (20,10), B(0,20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

Answer 1

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

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,S be the points which divide the line segment AB into five equal parts. 
 So,we observe that 
P divides AB in the ratio 1:4. 

Given:  A=(20,10) 
             B = (0,20) 

By Section Formula ,
$P(x,y) = (\frac{4*20+1*0}{4+1} , \frac{4*10+1*20}{4+1} ) =(16,12)$


3) Also,Q divides AB in the ratio 2:3 .

$Q(x,y)= (\frac{3*20+2*0}{4+1}, \frac{3*10+2*20}{4+1} )=(12,14)$


4) Also, R divides AB in the ratio 3:2 .
 
$R(x,y)= (\frac{2*20+3*0}{4+1} , \frac{2*10+3*20}{4+1} =(8,16)$


5)And S divides the AB in the ratio  4:1 . 

$S(x,y) = (\frac{1*20+4*0}{4+1} , \frac{1*10+4*20}{4+1}) =(4,18)$


Final Answer: Required co-ordinates are: 
 
$\boxed{(6,12),(12,14),(8,16),(4,18)}$

Answer 2

Answer:

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