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Lines, Parallel and Perpendicular Lines, Parallel and Perpendicular


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Answers:Perpendicular lines have the property that their slopes are the negative inverse of each other. If the slope of one line is "m", and the slope of the other is "-1/m", then the lines are perpendicular

Question:When they say a line is perpendicular to a plane, it means that the line is perpendicular to every line that passes through the point of intersection. Does this mean a line can be perpendicular to a line in a plane but not be perpendicular to another line in the the plane that passes thru the point of intersection?

Answers:Yes, a line that is not perpendicular to a plane, but passing through the plane, can be perpenducular to one specific line drawn on the plane. However, apart from this line other lines drawn on the plane would not be perpendicular.

Question:In the definition it says that a line is perpendicular to a plane when it is perpendicular to every line that passes the point in the plane. why do they even need to say this much, couldn't they say if it is perpendicular to one line that passes thru that point it is perpendicular to plane?

Answers:No. Tilt the plane about some line in the plane that passes through the point in the plane. The 'perpendicular' is still at right angles to this one, privileged line. But it is not perpendicular to any other line in the plane. In other words, given a plane P and a line L passing through a point in that plane, you can always find some line in P that is perpendicular to L. But only when you impose the restriction that ALL lines in P passing through the point are perpendicular to L do you fix L as perpendicular to P.

Question:What is the slope of a line perpendicular to the line: 4x+4y=-16 How to work this?

Answers:First you put this equation into y=mx+b form: (remember you have to get the y by itself) 4x+4y=-16 -4x -4x ____________ 4y=-16-4x _ _____ (I'm dividing by 4, to get y by itself) 4 4 y=-1x-4 (I switched the # to get to y= mx+b form) Then, to find a line perpendicular to this equation you have to change the slope to a positive. y=x-4 So, your slope is gonna be 1.

From Youtube

Parallel and Perpendicular Lines :Parallel and Perpendicular Lines

Constructing Perpendicular lines :The video explains how to construct a perpendicular line to a point and a perpendicular line through a point not on a line.