Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have such a problem :

I am given :

  • x,y
  • $\|a\|$
  • $\alpha$
  • $\vec{v}$ and $\|v\|$

I need to get the coordinates of point X1Y2.

enter image description here

share|improve this question

2 Answers 2

$$(x_1, y_1) = (x, y) + \frac{a}{\|v\|} \cdot R(\alpha) \cdot \vec{v}$$ Where $R(\alpha)$ is a rotation matrix.

share|improve this answer
    
@Patryk: This is a best answer for a fast result.+1 ;-) –  Babak S. Jan 6 '13 at 11:00

Use this fact that for two vector $v=(x_1,x_2),w=(y_1,y_2)$ we can evaluate $v.w$, the dot product of $v$ and $w$, by two ways. They are : $$v.w=x_1y_1+x_2y_2$$ and $$v.w=|v||w|\cos(\alpha)$$

Personally, I prefer @Karolis's answer but we can have an elementary approach according to what was given to us.

  • $||a||=\sqrt{(X-X_1)^2-(Y-Y_2)^2}$
  • $XX_1+YY_2=vw=||v||.||a||.\cos(\alpha)$

Above system have two equations of two unknowns. As you noted, we have $||a||,||v||,\alpha,X,Y$ so, put the known values and evaluate $X_1,Y_2$. I hope I could help.

share|improve this answer
    
Thanks a lot for this but if I am correct I will have an equation with 2 unknowns, right ? –  Patryk Jan 6 '13 at 0:50
    
@Patryk: Right. But you have a system of equation with 2 unknowns and I think after solving this system, you will get X1 and Y1. Tell me if you have any problem in it. ;-) –  Babak S. Jan 6 '13 at 6:36
    
Somehow I can't see the second equation. Can you edit your answer so that it is a bit more clearer :) ? –  Patryk Jan 6 '13 at 10:45
    
@Patryk: Sorry and forgive me for the delay. –  Babak S. Jan 6 '13 at 21:02
    
Good job explaining! +1 –  amWhy Feb 23 '13 at 0:07

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.