I have a rectangle in geometric plane defined with x,y coordinates of 4 points (ABCD). Now one point (C) is moved to new x,y location and consequence is resizing of rectangle in a way that diagonal opposed point (A) remains still (stationary) but two neighboring points (BD) of the rectangle must be appropriately recalculated to maintain rectangular shape. Calculating is simple if rectangle is not rotated, but how to calculate points if rectangle is rotated.... for example 31 degrees ?
Rectangle points - resizing rectangle after one corner point is moved
- Thread starter TomazB
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mmm4444bot
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Try googling keywords, like rotating xy-coordinate system.
There are different methods. Here's one set of formulas for converting back and forth between (x,y) and (x', y').
(Click thumbnail, for larger image.)
There are different methods. Here's one set of formulas for converting back and forth between (x,y) and (x', y').
(Click thumbnail, for larger image.)
Tnx mmm4444bot.
I did google and I am aware of the angular functions.
I also believe that to You link among stated methods and unknown point coordinates is perfectly clear. But here I am a little short.
Please can you directly write methods in steps to calculate xy coordinates of point B1 (or D1) in picture. I have just x and y coordinates
of ABCD points and also the new coordinates of C1 point which is the reason for resize of rectangle.
I did google and I am aware of the angular functions.
I also believe that to You link among stated methods and unknown point coordinates is perfectly clear. But here I am a little short.
Please can you directly write methods in steps to calculate xy coordinates of point B1 (or D1) in picture. I have just x and y coordinates
of ABCD points and also the new coordinates of C1 point which is the reason for resize of rectangle.
D
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In which class were you given this problem? What is your math background?
There is no class. It is my own programing project and I have high school but 40 years ago and I am a little rusty. However, this is not related to the question so if you can help ....
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We ask about students' backgrounds and current area of study, because this often helps us understand what the issues are, or what sort of solution is expected by the instructor. (For instance, there are problems that one learns to solve one way in algebra, and another way in calculus.)
You are given the coordinates of C1. You know that A1 is on (an extension of) the line AB. You can find the slope of BC (here), and use C1 as your plug-in point, to obtain the equation of the line through B1 and C1. (here) You can also find the slope of AB, and use either A or B to find the equation of the line for that side of the rectangle.
You now have two lines' equations, and those two lines intersect at A1. So solve the system of equations (here) to find those coordinates.
Follow the same steps for the slope of CD, the equation through AD (having the same slope as BC) using point A or B. The line through CD is parallel to the line through D1 and C1. Use this information (and the point C1) to find the equation of that line. The lines AD and C1D1 intersect at D1. Solve the system to find the coordinates of that point.
If you get stuck, please reply showing all of your work so far. Thank you!
