SOLUTION: Find the point on the y axis that is equidistant from (5,1) and (-3,-1).

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Question 1121605: Find the point on the y axis that is equidistant from (5,1) and (-3,-1).
Found 2 solutions by solver91311, josgarithmetic:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Find the midpoint of the segment that has the given points as endpoints. Use the negative reciprocal of the slope of the segment joining the two given points and the midpoint to derive, with the use of the Point-Slope form of an equation of a line, an equation of the perpendicular bisector of the segment joining the two given points. Since any point on a perpendicular bisector of a segment is equidistant from the endpoints of the segment, all you need to do is determine the -intercept of the perpendicular bisector.


John

My calculator said it, I believe it, that settles it

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
A point on the y-axis will have x=0.
The point can be the ordered pair (0,y).

Point (0,y) is same distance from (5,1) as from (-3,-1).

Using the Distance Formula,



sqrt%2825%2B%28y-1%29%5E2%29=sqrt%289%2B%28y%2B1%29%5E2%29

25%2By%5E2-2y%2B1=9%2By%5E2%2B2y%2B1

16-2y=2y

16=4y

highlight%28y=4%29
The point asked for is (0,4).