SOLUTION: Let A= (1,5) and B=(3,-1) Find two points that are equidistant from A and B. Describe all such points

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Question 821813: Let A= (1,5) and B=(3,-1) Find two points that are equidistant from A and B. Describe all such points
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
The points which will be equidistant from A and B will be on a line that is perpendicular to segment AB and which passes through the midpoint of segment AB. (This can be used as the requested description.)

Here's how to find two of those points:
  1. Use the midpoint formula to find the midpoint between A and B. This can be used as one of the two points.
  2. Find the slope of segment AB.
  3. Find the slope for a perpendicular to segment AB. (Since slopes of perpendiculars are negative reciprocals of each other, just take the slope from the previous step, flip it upside down and change its sign.)
  4. Use the midpoint and the slope of a perpendicular to step to another point. For example, if the midpoint was (1, 8) and the slope of the perpendicular is (-2)/3, then from (1, 8) go down 2 and to the right by 3, ending up at (-1, 11). Whatever you get from this can be your second point.
P.S. If you want/need the equation the the line which contains all the points which are equidistant from A and B, then use the midpoint (from step 1) and the slope of the perpendicular (from step 3) and find the equation of the line with that slope and which passes through the midpoint.
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