# Math Help - Quick Line (just made it up for fun)

1. ## Quick Line (just made it up for fun)

Any Two points (and an x and y axis) can form two "Quick" lines (except under three circumstances), can anyone figure out how the lines are determined (you can move the points around)?

hint: My teacher's been making us do things with patty paper.

PS: if you don't have enough information to figure it out, please tell me.
The Two points are the opposite corners of the smallest possible rectangle that touches them. When that rectangle is folded such that the two points lie on top of each other than the line connects the two non-dotted corners

Let's see who's the first to find it.

2. Originally Posted by Quick
Any Two points (and an x and y axis) can form two "Quick" lines (except under three circumstances), can anyone figure out how the lines are determined (you can move the points around)?

hint: My teacher's been making us do things with patty paper.

PS: if you don't have enough information to figure it out, please tell me.

Let's see who's the first to find it.
It looks like the tangent of the angle?

3. Originally Posted by ThePerfectHacker
It looks like the tangent of the angle?

I don't know what a tangent of an angle is...

4. Originally Posted by Quick

I don't know what a tangent of an angle is...
When a line intersects a x-axis is creates an angle. The tangent of that angle ( $\tan \theta$) is the slope of the line. It seems that the slope of those lines is the tangent of the angle they create.

5. Originally Posted by ThePerfectHacker
When a line intersects a x-axis is creates an angle. The tangent of that angle ( $\tan \theta$) is the slope of the line. It seems that the slope of those lines is the tangent of the angle they create.
I don't think it is, at least it isn't when the line is 45 degrees to the horizontal (it should be -1 instead of 1)

The answer is in white text in my original post. (so noone quote my original post)

6. This is what I think: The two lines are at right angle to the line imagined line between the two points. Then, if the two points is (x1, y1) and (x2, y2), the two lines goes through the points (x1, y2) and (x2, y1) respectively.