SOLUTION: PLEASE ME. FIND THE POINT EQUIDISTANT FROM (-6, -1) AND (-1, 2) AND AT A DISTANCE 5 FROM (-2, 7). THANKS IN ADVANCE

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Question 867626: PLEASE ME. FIND THE POINT EQUIDISTANT FROM (-6, -1) AND (-1, 2) AND AT A DISTANCE 5 FROM (-2, 7). THANKS IN ADVANCE
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Find midpoint of the first two points.
x=-7%2F2, y=1%2F2.
Slope of the first two points, %282-%28-1%29%29%2F%28-1-%28-6%29%29=3%2F5.
The LINE containing all points equidistant from those two first given points is y=-%285%2F3%29x%2Bb, and you can find b using either of those two given points.
b=y%2B%285%2F3%29x=-1%2B%285%2F3%29%28-6%29=-2%2A5-1=-11;
The equation of the needed line is then highlight%28y=-%285%2F3%29x-11%29.
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Notice that the two slopes are negative reciprocals of each other. %283%2F5%29 versus -5%2F3.

Now you have a variable point ( x, -(5/3)x-11 ) which is 5 units distance from the point (-2, 7). Arrange these in the Distance Formula to solve for the x coordinate (two of them) for this particular point(s) on the line of y=-%285%2F3%29x-11.
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I have not finished, but only explained what to do for finishing.