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can somebody help me with this by giving me a hint how to solve these $2$ $?$:

Given

  • a point $P$ with coordinates $(10,4)$ in a fixed coordinate system.

  • a new coordinate system with origo in $(6,0)$ and rotated $60^{\circ}$ counterclockwise.

$1$) Find the coordinates of $P$ in the new coordinate system.

$2$) Write down the equation, that will transform any point $P=(x,y)$ in the fixed coordinate system to coordinates $P'=(x’,y’)$ in the new coordinate system.

This is what I have thought about: Finding the coordinates as projections and then I don't know because I don't understand what I have. Do I've $2$ coordinates$?$

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  • $\begingroup$ The value of the x coordinate of P in the old system is 10. What is its value in the new coordinate system? And that of y? $\endgroup$
    – MASL
    Commented Sep 22, 2015 at 18:21
  • $\begingroup$ Consider now another arbitrary point in that in the old system has coordinates (2,3). What are its x and y values in the new system? $\endgroup$
    – MASL
    Commented Sep 22, 2015 at 18:24
  • $\begingroup$ Finally, consider an arbitrary point $(x_o,y_o)$ in the old system. Can generalize from the above examples and write the values of (x,y) in the new system in terms of $x_o,\,y_o$? $\endgroup$
    – MASL
    Commented Sep 22, 2015 at 18:25
  • $\begingroup$ Do I have to say 10-2=x and 4-3=y ? $\endgroup$
    – Mr.H123
    Commented Sep 22, 2015 at 18:25
  • $\begingroup$ No. Ok, let's start with something easier. Consider the real line, from $-\infty$ to the left to $+\infty$ to the right, and a point $P$ at $x=10$. No suppose I move the origin of coordinate and locate it where before was $6$. What's the location of $P$ now? $\endgroup$
    – MASL
    Commented Sep 22, 2015 at 18:30

1 Answer 1

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When origin located at $O=(0,0)$: $P=(x_o,y_o)$

Location of new origin: $O'=(a,b)$

Point $P$ in new system: $P=(x_o,y_o)-(a,b)=(x_o-a,y_o-b)$

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  • $\begingroup$ However, if you don't try to solve and understand the questions I asked you before, no formula will really be helpful. You need to understand that on a paper by drawing it all!! $\endgroup$
    – MASL
    Commented Sep 22, 2015 at 21:30
  • $\begingroup$ the new x is 4 as 10-6=4 $\endgroup$
    – Mr.H123
    Commented Sep 22, 2015 at 23:09
  • $\begingroup$ You got it. If this helped you it would be nice if you accept and/or upvote this answer. Thanks. $\endgroup$
    – MASL
    Commented Nov 20, 2015 at 14:45

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