InterviewSolution
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InterviewSolution
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The distance of the point (1, 3) from the line `2x+3y=6`, measured parallel to the line `4x+y=4`, isA. `5/sqrt(13)` unitsB. `3/sqrt(17)` unitC. `sqrt(17)` unitsD. `sqrt(17)/2` units |
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Answer» Correct Answer - D The line `4x+y=4` can be written as `y=-4x+4`. So, slop is -4. The line parallel to `4x+y=4` will have slope `-4` only. Given point `=(1, 3)` Equation of line passing through (1, 3) and slope -4 is `y-3=-4(x-1)` `implies y-3=-4x+4 implies 4x+y=7`. Solving the two equations, we get `2x+3y=6 implies 4x+6y=12` `{:(4x+y=7),(cancel((-))(-) (-)),(bar(5y=5implies y=1)):}` `2x+3y=6 implies 2x+3(1)=6` `implies 2x=3 implies x=3/2`. Distance between the points (1, 3) and `(3/2, 1)` is `sqrt((3/2-1)^(2)+(1-3)^(2))=sqrt((1/2)^(2)+(-2)^(2))=sqrt(1/4+4)=sqrt(17/4)=sqrt(17)/2`. |
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