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Question 544659: Name a point that is sqrt(2)away from (-1,5).
Name a point that is between 50 and 60 units away from (7,-2) and state the distance between from the two points.
Could you show me how to work them out? Please?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
All points a given distance from a given point is a circle where the given point is the center. The equation of a circle with center at the point ) and radius  is ^2\ (y\ -\ k)^2\ =\ r^2)
So any point where the coordinates of the ordered pair identifying that point satisfy
\right)^2\ +\ \left(y\ -\ 5\right)^2\ =\ 2)
is, by definition of a circle, the radius, i.e.  , distant from the given point (-1, 5).
There are two ways to proceed. You can pick any value you like for either  in the interval  or  in the interval  , substitute that value, and then solve for the value of the other variable, giving you an ordered pair that is on the circle and the proper distance from the given point.
Or you can do it the easy way: Replace the coordinate -1 in the given point with either  or  OR replace the coordinate 5 in the given point with either  or  .
John
My calculator said it, I believe it, that settles it
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