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Which of the following is correct in respect of the equations `(x-1)/2=(y-2)/3` and `2x+3y=5` ?A. They represent two lines which are parallel.B. They represent two lines which are perpendicular.C. They represent two lines which are neither parallel nor perpendicular.D. The first equation does not represent a line.

Answer» Correct Answer - B
Given equation of line is
`(x-1)/2=(y-2)/3`
`implies 3x-3=2y-4 implies 3x-2y+1 =0`
`implies y=(3x)/2+1/2`
and equation of second line is `2x+3y=5`
`implies y=(-2)/3 x+5/3`
`:.` Slope of first line, `m_(1)=3/2`
and slope of second line, `m_(2)=-2/3`
`:. m_(1)m_(2)=-1`
Hence, two lines are perpendicular to each other.


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