Question 382943: Find the center of a circle with these three points: (-7,9)(-13,3)(-1,3).
Found 3 solutions by Alan3354, Fombitz, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the center of a circle with these three points: (-7,9)(-13,3)(-1,3).
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2 points, (-13,3) & (-1,3), are on a line parallel to the x-axis. The 3rd point, (-7,9) is equidistant from the 1st 2, so the 1st 2 points are on the ends of a diameter.
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The midpoint is the center, = (-7,3)
Answer by Fombitz(32388)  (Show Source):
Answer by Edwin McCravy(20065)  (Show Source):
You can put this solution on YOUR website! (-7,9)(-13,3)(-1,3).
Let's plot those three points:
Now let's draw the chord from (-13,3) to (-1,3). I'll draw it in green:
Now the perpendicular bisector of a chord must go through the center
of a circle. Since the green chord is 12 units long and is horizontal,
its midpoint is 6 units left of (-1,3) and 6 units right of (-13,3).
So the midpoint of that chord is (-7,3). So we draw the perpendicular
bisector of the green line. I'll draw it in red:
Now since the third point
has the same x-coordinate -7, that means that the perpendicular bisector
of the green chord goes through that third point (-7,9). Notice that
(-7,9) is exactly 6 units above (-7,3), and that the other two given
points are also exactly 6 units from (-7,3), so that means that the
circle's center IS the point (-7,3) and the green chord is a diameter of
the circle. So (-7,3) is the center and the radius is 6. And we can draw
in the circle with center (-7,3) and radius 6:
Answer: center (-7,3).
Edwin
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