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Maybe it's not a question for IIT, but I need to know the answer urgently. It would be great if you could help. It is a data sufficiency question. Could you please explain the answer. Also, if you are aware of any formula related to the reflection of a line about x-axis, or about y-axis or about any other line, please let me know. thanks Q. A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n? (1) m = p + 2 (2) m = 3p

Maybe it's not a question for IIT, but I need to know the answer urgently. It would be great if you could help. It is a data sufficiency question. Could you please explain the answer. Also, if you are aware of any formula related to the reflection of a line about x-axis, or about y-axis or about any other line, please let me know. thanks


Q.


A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

(1) m = p + 2

(2) m = 3p



Grade:

1 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

y=px+q is inclined at tan-1p to x-axis, y=x is angle bisector of y=px+q and its reflection, angle between y=x and y=px+q is

(π/4)-tan-1p this is equal to angle between y=x and the reflection of y=px+q over y=x

therefore angle between reflection and x-axis= (pi/4)+(pi/4)-tan-1p=(pi/2)-tan-1p=cot-1p, slope of this line=(1/p)=m

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