SOLUTION: a point is at a distance 4 sqrt of 2 units from (-3/2,-5/2) and at a distance 2 sqrt of 5 units from (9/2,-5/2), find the point

Question 774946: a point is at a distance 4 sqrt of 2 units from (-3/2,-5/2) and at a distance 2 sqrt of 5 units from (9/2,-5/2), find the point
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a point is at a distance 4 sqrt of 2 units from (-3/2,-5/2) and at a distance 2 sqrt of 5 units from (9/2,-5/2), find the point
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Draw a circle around each given point with the radius = the given distance.
The points (2 of them) will be the intersections of the circles.
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a distance 4 sqrt of 2 units from (-3/2,-5/2) -->
a distance 2 sqrt of 5 units from (9/2,-5/2) -->
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Lucky the y terms are equal

------------------------------ Subtract

x = 5/2
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Sub for x into either eqn, find 2 values for y

Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
[ a point is at a distance units from (-3/2,-5/2) and at a distance units from (9/2,-5/2), find the point ]

This point is unknown (x,y).

Look for one or two triangles with one side units long, and two other sides which are the two given lengths:
--------------------------------------------

_______We can make more use of this one.
which is a circle

_______ .
also a circle

These two circles both contain the expression , which give us a way to relate them.

What you now want to do, is go back to this same circle equation, solve it for y, and assign x=2 and find the value for y. You will get two solutions for this y. Whatever y is found to be, the two points wanted will be (2, y) and (2, -y).

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