# Rotation and Transformation of Axes

• Mar 14th 2010, 10:48 AM
truevein
Rotation and Transformation of Axes
Hi,I have a question that I have problems with.It's my homework due Thursday.

M1(9,-3);M2(-6,5).Bring the origin to M2 and rotate the system so that M1,M2 agrees with the direction of the new x axis.(tanθ=-8/15).

I can't understand what I'm supposed to find as a solution.Why do I need to change the origin?Should I only show how I did it?Thanks in advance.(I'm not asking for having my hw done by sb else.I studied all weekend on this subject but I can't understand the question.)
• Mar 16th 2010, 01:15 AM
smig1973
Rectangular to Polar Co-ordinates
[quote=truevein;474315]Hi,I have a question that I have problems with.It's my homework due Thursday.

M1(9,-3);M2(-6,5).Bring the origin to M2 and rotate the system so that M1,M2 agrees with the direction of the new x axis.(tanθ=-8/15).

[This is simply a variation on pythagorus theorum. Firstly, by bringing the origin to M2 (that is to say applying +6 and -5 respectively to the co-rdinates of both M1 & M2) the resultant values for M1 are now also the difference values as follows;

XM1-XM2=15 and YM1-YM2=-8

From these you can define a bearing (or azimuth) from M2 to M1;

TANθ=15/-8 so ATAN(15/-8)= -61.9275 (Decimal Deg)

Note now that your new bearing has simply swaped the X and Y difference values which means that the axis has rotated thro 90Deg (100Grad).

TANθ=-8/15 so ATAN(-8/15)= -28.0725 (Decimal Deg)

And if you require a distance;

SQRT(15^2 + (-8)^2) = 17

which is the same as

SQRT((-8)^2 + 15^2) = 17]
• Mar 16th 2010, 07:16 AM
truevein
Thank you so very much :)
• Mar 17th 2010, 06:52 AM
smig1973
You're not alone!
You're quite welcome. And don't worry about not getting to grips with the problem straight away. I currently have to spend quite some time on a regular basis explaining this and other plane geometry principals to graduate civil engineers at my office, so you're not alone. Feel free to ask the questions if you get stuck again.
• Mar 18th 2010, 01:31 AM
truevein
Thanks again!Then I can ask some other questions at the weekend:D-if you don't mind-I'll study again to fully understand it and there will absolutely be questions that I'll have problems with.(Bow)(Bow)(Bow)