What if P and Q have both the same x-coordinate and y coordinate? In that case, there will be no right angle QPR. The same goes to R and P. What's wrong in that reasoning?
Good question! If P and Q had the same x and y coordinate, they would be the same point. In that case, we would not have a triangle but rather a line segment from P/Q to R. This would also be the case if R and P shared both their x and y coordinate. The two points would be the same point and on the coordinate plane, we would observe a line segment from R/P to Q.
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