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CBSE Class 10 Answered

Page 353. Question : 10 The line joining the points (3, -2 ) and -3,-4) is trisected equally. Find the coordinates of the points of trisection
Asked by miniprasad | 20 Oct, 2018, 04:25: PM
answered-by-expert Expert Answer
 
 
 
 
Let A= (3, -2) and B = (-3, 4)
and the coordinates of trisected points are C = (a1 , b1) and D= (a2 , b2) 
 
Given that the line joining the points (3, -2 ) and -3,-4) is trisected equally.
begin mathsize 16px style rightwards double arrow AC over BC equals space BD over AD space equals space 1 half
By space Section space Formula comma space we space get
open parentheses straight x comma space straight y close parentheses space equals space open parentheses fraction numerator mx subscript 2 space plus space nx subscript 1 over denominator straight m space plus space straight n end fraction comma fraction numerator my subscript 2 space plus space ny subscript 1 over denominator straight m space plus space straight n end fraction close parentheses space
Here space comma space straight m space equals space 1 space and space straight n space equals space 2
open parentheses straight x subscript 1 comma space straight y subscript 1 close parentheses space space equals space left parenthesis 3 comma space minus 2 right parenthesis space and space open parentheses straight x subscript 2 comma space straight y subscript 2 close parentheses space equals space left parenthesis space minus 3 comma space minus 4 right parenthesis
open parentheses straight a subscript 1 comma space straight b subscript 1 close parentheses space space equals open parentheses 5 over 3 comma space fraction numerator negative 8 over denominator 3 end fraction close parentheses space
and space straight D space is space the space mid space point space of space straight B space and space straight C space comma space thus
open parentheses straight a subscript 2 comma space straight b subscript 2 close parentheses space space equals open parentheses fraction numerator negative 2 over denominator 3 end fraction comma space 2 over 3 close parentheses
Therefore space the space points space of space trisection space are space open parentheses 5 over 3 comma space fraction numerator negative 8 over denominator 3 end fraction close parentheses space and space open parentheses fraction numerator negative 2 over denominator 3 end fraction comma space 2 over 3 close parentheses. end style
 

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