SOLUTION: A diameter of a circle has endpoints at (4, 6) and the origin. Which point is also on the circle? A. (�1, 2) B. (6, 3) C. (5, 0) D. (�1, 1) E. NOTA Please explain.

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Question 558049: A diameter of a circle has endpoints at (4, 6) and the origin. Which point is also on the circle?
A. (�1, 2) B. (6, 3) C. (5, 0) D. (�1, 1) E. NOTA
Please explain.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The center of the circle is the midpoint of the diameter segment. Use the midpoint formulas to calculate the coordinates of the center of your circle.

and

Once you have the coordinates of the center, use the distance formula to find the distance from either endpoint to the center, which is to say the radius of the circle.

where and are the coordinates of the given points.

Then use the distance formula to calculate the distance from the center to each one of the points given as answers. If any of them give a distance equal to the radius, then perforce the point must be on the circle.

John

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