find the ratio in which the line 3x+y-9=0 divides the line segment joining the points (1,3) and (2,7)

Asked by tarjindersingh55 | 2nd Oct, 2017, 11:51: AM

Expert Answer:

begin mathsize 16px style Suppose space the space line space 3 straight x plus straight y minus 9 equals 0 space divides space the space line space segment space joining space straight A left parenthesis 1 comma space 3 right parenthesis space and space straight B left parenthesis 2 comma space 7 right parenthesis
in space the space ratio space straight k space colon space 1 space at space point space straight C.
Then comma space the space coordinates space of space straight C space are space open parentheses fraction numerator 2 straight k plus 1 over denominator straight k plus 1 end fraction comma space fraction numerator 7 straight k plus 3 over denominator straight k plus 1 end fraction close parentheses.
But comma space straight C space lies space on space 3 straight x plus straight y minus 9 equals 0.
Therefore comma
3 open parentheses fraction numerator 2 straight k plus 1 over denominator straight k plus 1 end fraction close parentheses plus fraction numerator 7 straight k plus 3 over denominator straight k plus 1 end fraction minus 9 equals 0
rightwards double arrow 6 straight k plus 3 plus 7 straight k plus 3 minus 9 straight k minus 9 equals 0
rightwards double arrow 4 straight k minus 3 equals 0
rightwards double arrow straight k equals 3 over 4
So comma space the space required space ratio space is space 3 space colon space 4 space internally. end style

Answered by Rashmi Khot | 3rd Oct, 2017, 09:22: AM

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