# Finding the position vector for translated frame of reference

• simphys

#### simphys

Homework Statement
Please refer to the picture, I don't really have a question problem.
I was posed the question on how I would model what the position would be when the frame of reference is translated as shown on the picture.
Relevant Equations
##\vec r = 8t \hat i + 6t \hat j## for the y-x reference framse.
what would be the y'-x' ##\vec r## vector be?

I think it is
##\vec r = (8t - 1) \hat i + (6t - 2) \hat j## (not sure whether it is correct or not.)
I thought about it as at t = 0 the position needs to be -1i -2j so that is why I took the signs in the y'-x' frame position vector as a - instead of + signs for 1 and 2.

Is it ok to reason like this or do I need to derive it from somewhere else? I am not very acquianted with translation of the axes that's why I am asking. • Delta2
What is the origin of x' y' system as measured in the x y system?

• simphys
What is the origin of x' y' system as measured in the x y system?
in points (1,2) = (x,y) can you find a relation for the vectors ## \vec R##, ##\vec r## and ##\vec r\:'##?

• • Delta2 and simphys
What is the origin of x' y' system as measured in the x y system?
oh wait, isn't this actually the 'relative frames of references' that are used to describe relative motion?
than it becomes r_x/p = r_x'/x + r_p/x' (where the condition was that it should be an inertial frame aka cst velocity or at rest for it to be valid)

• malawi_glenn
View attachment 304325
can you find a relation for the vectors ## \vec R##, ##\vec r## and ##\vec r\:'##?
yep exactly my post #5 no?

aka cst
?

• simphys
?
constant, apologies.

constant, apologies.
np glhf

• • simphys and Delta2