I have three points defining the vertices of a triangle A(1,4) B(6,7) C(5,1)
I have found that vector AC has a slope(m) of 0.6 and vector BC has a slope of 6. From these slopes have the angles of ≈34.39° and ≈73.94° respectively. Based on this, I know that these vectors intersect to form angle B at ≈39.55°. I would like to relocate vertex B so that angle B becomes 90° and therefore, ∠ABC becomes a right-angle.
The solution is constrained by the fact that:
- I don’t wish to relocate vertex A or C.
- I would like to adjust the location of B while attempting to keep the degree of adjustment relative to vertex A and C proportionate.
Being a geographer, I attempting to implement this solution using Geographic Information Systems (GIS) so I am not extremely proficient with math. Below is my logic for solving this problem but I haven’t had any success so far, so please post your proposed solution. Thanks!
Essentially, I am attempting to adjust the slopes of vector AC and BC so that angle B is affected and becomes 90°.
-At first I attempted to sum the component angles and find the difference from 90° and identify those points that do not intersect at a right-angle. I then tried to find what the new angles of the vectors should be by dividing each angle by the sum and multiplying by 90. I thought that by doing this I could find a ‘proposed’ new angle of the subject line.
Ex. (angleAC/(angleAC+angleBC))*90 = angleACnew
Using the new ‘proposed’ angle I would convert this back to a slope value and apply this to each of the vector equations and setting the equations equal to each other and algebraically solve for x.
I then planned on subbing back into one of the equations and solving for y. Thereby, giving be the new x,y coordinate for point B where B was a 90° angle. However, I realized that this methodology does not work since the sum of angleAC and angleBC do not accurately reflect the internal angles of the triangle and therefore do not yield a logical “adjustment value”.
Does anyone have some suggestions and/or guidance?