1
$\begingroup$

I have 3 points and their coordinates $(A, B, C)$. Then I have new coordinates of points $A'$ and $B'$ How to calculate the coordinates of point $C'$ knowing that the distance from point A to point C and the angle between line AB and line AC is the same. It must work as a formula in any program or on a sheet of paper.

Available

Point $A$ (the $x$ and $y$ coordinate) Point $B$ (the $x$ and $y$ coordinate) Point $C$ (the $x$ and $y$ coordinate) Point $A'$ (the $x$ and $y$ coordinate) Point $B'$ (the $x$ and $y$ coordinate)

$|A−C|=|A′−C′|$ but $|A−B|$ don't equal $|A′−B′|$

Angle between $AC$ and $AB$ is the same as $A'C'$ and $A'B'$

Unknown

All Angles

Point $C'$ (the $x$ and $y$ coordinate)

My conclusions

$AB=\sqrt{(Bx−Ax)^2+(By−Ay)^2}$

$AC=\sqrt{(Cx−Ax)^2+(Cy−Ay)^2}$

$CB=\sqrt{(Bx−Cx)^2+(By−Cy)^2}$

$A'B'=\sqrt{(B'x−A'x)^2+(B'y−A'y)^2}$

$\endgroup$
  • $\begingroup$ In the triangle formed by A', B' & C' we only know one side and one angle. So the given information is insufficient to find the coordinates of C'. $\endgroup$ – Wishwas Jul 4 at 8:34
  • $\begingroup$ But we also know the distance of Point C''; from Point A'';, which gives sufficient information to create a vector at the end of which Point C''; will be located. I just don't know how to make it. $\endgroup$ – Joachim Biernacki Jul 4 at 8:43
  • $\begingroup$ Step 1. Shift origin to A'. Step2. Rotate Axis so that A'B' is along X-axis. Now A'C' is a line making a known angle with X-axis. Now C' a point on this line at a known distance from the current origin. So you get its co-ordinates. Now reverse the rotation in step 2. Reverse the shift of origin done in step 1. $\endgroup$ – Wishwas Jul 4 at 9:28
  • $\begingroup$ I don't understand how to do it in maths. $\endgroup$ – Joachim Biernacki Jul 4 at 9:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.