Question 135980: I am trying to establish the correct equation for
The points (1,5), (4,5), and (1,0) represent three corners of a rectangle; find the coordinates of the fourth point.
For obvious reasons I concluded that the fourth point is (4,0), but I am unsure how to present this.
m = y4 - y3 – y2 – y1/x4 - x3 – x2 – x1
m = 5 – 5 – 0 – 5/1 – 4 – 1 – 4
Thanks!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Since you have three vertices of the rectangle, you have two sides defined, namely the line segment from (1,5) to (4,5) and the line segment from (1,5) to (1,0). The segment from (1,5) to (4,5) must be parallel to the segment between (1,0) and your missing point (x,y), and the segment from (1,5) to (1,0) must be parallel to the segment between (4,5) and your missing point (x,y).
Since the y coordinates of (1,5) and (4,5) are equal, the equation for the line containing the line segment connecting these two points must be the equation of a horizontal line, namely  . Since the segment between (1,0) and (x,y) is parallel to this line, it must be a horizontal line as well, and since the y-coordinate of one of the points is 0, all of the y-coordinates must be 0 and the equation must be  .
Using similar logic, the equation for the segment from (1,5) to (1,0) must be  and therefore the equation for the segment from (4,5) to (x,y) must be  .
Hence your point is the intersection of the two lines represented by and , so the ordered pair is the solution set of the system:
Which is (4,0)
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