Not sure your in the right classification. The most useful formulation would be in the expression for the tangent of the difference of two angles.
Consider two straight lines L1 (y = 2x +1) and L2 (y=x).
a) What is the slope of line L1 in respect to line L2?
b) What is the equation of line L1 in respect to line L2?
NOTE. Think that the original xy co-ordinate system has been
rotated in respect to the origin so that line L2 defines the new
x-axis x´ and y´ is the new y-axis!
now i know the slope of line 1 is 2 and line 2 is 1. im not sure if thats the kind of answer they want for part a of the question. and part b im not sure at all what they are asking for. PLease help me understand this sort of problem.
thank you
ok from what i get is i first of course graph the 2 lines the first obvioulsy intersecting at 1,0 on the x axis and the 2nd at 0,0. i can conclude that they intersect at point (-1,-1). Now the only thing i do not understand is the rotation and how you came up with . what theorum or rule is that called? i do not rememebr learning this so this is new to me. but of course it works to get the new (0,0) point for the new axis by plugging in -1 for x and y and using . just i guess the only thing is like i said i need to know why to use the formula to get it if you could tell me that would be appreciated
Finding the angle as you rotate y= x to the x-axis is exactly the same as finding the angle between the lines themselves.
I would use the dot product: The vector <1, 1> is in the direction of the line y= x. The vector <1, 2> is in the direction of the line y= 2x+ 1. Their dot product is where is the angle between the lines. and so, finally, .
You could use a calculator to find the angle and then the tangent but you could also say .
Perhaps simplest, though, is to use the formula . Here, tan(x)= 2 and tan(y)= 1 so !