In what ratio does the line x-y-2=0 divide the line segment joining the points (3,-1) and (8,9)? Also find the point of division .

Asked by Adrija | 12th Nov, 2017, 03:42: PM

Expert Answer:

begin mathsize 16px style Let space straight A identical to left parenthesis 3 comma negative 1 right parenthesis space and space straight B identical to left parenthesis 8 comma 9 right parenthesis
Let space the space line space straight x minus straight y minus 2 equals 0 space divide space the space line space segment space AB space at space point space straight C left parenthesis straight x comma straight y right parenthesis space in space the space ratio space straight m colon straight n.
By space section space formula comma
straight C left parenthesis straight x comma straight y right parenthesis equals open square brackets fraction numerator straight m cross times 8 plus straight n cross times 3 over denominator straight m plus straight n end fraction comma space fraction numerator straight m cross times 9 plus straight n cross times left parenthesis negative 1 right parenthesis over denominator straight m plus straight n end fraction close square brackets equals open square brackets fraction numerator 8 straight m plus 3 straight n over denominator straight m plus straight n end fraction comma space fraction numerator 9 straight m minus straight n over denominator straight m plus straight n end fraction close square brackets
Since space point space straight C left parenthesis straight x comma straight y right parenthesis space lie space on space line space straight x minus straight y minus 2 equals 0 comma
fraction numerator 8 straight m plus 3 straight n over denominator straight m plus straight n end fraction minus fraction numerator 9 straight m minus straight n over denominator straight m plus straight n end fraction minus 2 equals 0
rightwards double arrow 8 straight m plus 3 straight n minus 9 straight m plus straight n minus 2 straight m minus 2 straight n equals 0
rightwards double arrow negative 3 straight m plus 2 straight n equals 0
rightwards double arrow 3 straight m equals 2 straight n
rightwards double arrow straight m over straight n equals 2 over 3
Hence comma space line space straight x minus straight y minus 2 equals 0 space divide space the space line space segment space joining space straight A left parenthesis 3 comma negative 1 right parenthesis space and space straight B left parenthesis 8 comma 9 right parenthesis space in space the space ratio space 2 colon 3. end style

Answered by  | 7th Dec, 2017, 02:25: PM

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