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Let say we have a $2$D coordinate and a circle, the center is at origin and a straight line passes through the circle.

Let one coordinate is $(-3,3)$ and other we have to find the other coordinates$(x,y)$, where a straight line cuts the opposite side of coordinate$(-3,3)$. the straight line passes through the origin.

According to the above coordinates, the answer will be $(3,-3)$.

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  • $\begingroup$ Welcome to MSE. Could you please show some of the work that led you to believe the answer is $(3,-3)$? Showing your work is a good habit to get into on this site. $\endgroup$ – Robert Howard Aug 7 '18 at 16:57
  • $\begingroup$ This is unclear to me. Perhaps rephrasing, giving different names to different things, and breaking this long sentence into several simple ones would help. $\endgroup$ – Arnaud Mortier Aug 7 '18 at 17:02
  • $\begingroup$ Sorry the equation of line is x=y. $\endgroup$ – Avnish Gupta Aug 7 '18 at 17:04
  • $\begingroup$ Don't you mean $x=-y?$ $\endgroup$ – saulspatz Aug 7 '18 at 17:12
  • $\begingroup$ Are you asking whether your answer is correct? Why are you unsure? $\endgroup$ – saulspatz Aug 7 '18 at 17:14
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You know that the center of the circle is at origin. Now you can use the parametric form of the coordinates of a point on a straight line. Which tells the coordinates of two points on a straight line(in our case: the diameter under consideration) and a given point. Now we can use : Coordinates (x±rcosA,y±rsinA) where r is the radius of the circle. This is the best way to know it, according to me.

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