Algebra Examples

Find the Circle Using the Diameter End Points
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. The given end points of the diameter are and . The center point of the circle is the center of the diameter, which is the midpoint between and . In this case the mid point is .
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Use the midpoint formula to find the midpoint of the line segment.
Substitute in the values for and .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by to get .
Add and to get .
Add and to get .
Divide by to get .
Find the radius for the circle. The radius is any line segment from the center of the circle to any point on its circumference. In this case, is the distance between and .
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Use the distance formula to determine the distance between the two points.
Substitute the actual values of the points into the distance formula.
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Subtract from to get .
Remove parentheses around .
Raising to any positive power yields .
Multiply by to get .
Subtract from to get .
Remove parentheses around .
Raising to any positive power yields .
Add and to get .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is the equation form for a circle with radius and as the center point. In this case, and the center point is . The equation for the circle is .
The circle equation is .
Simplify the circle equation to get .
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