Pregunta
Solve for the Area, center, radius and standard equation using the endpoints of a diameter.
Center (using midpoint formula)
Area ofthe Clrele
un 13
Radius (use center as
And any point from the diameter will serve as
Center (using midpoint formula)
Ask by Murphy Harrington. in the Philippines
Jan 12,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
To find the center, radius, area, and standard equation of a circle using the endpoints of its diameter:
-
Center (Midpoint):
-
Radius:
-
Standard Equation:
-
Area:
Example:
For points and
:
For points
- Center:
- Radius:
units - Standard Equation:
- Area:
square units
Solución

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Como
The Deep Dive
To find the center of the circle using the midpoint formula, you’ll first add the x-coordinates of the endpoints of the diameter and divide by 2 for
. For
, add the y-coordinates of the endpoints and divide by 2. This will give you the coordinates of the center. The area of the circle is given as
, and if the radius is stated to be
, then the area would be
.
Next, to find the radius, take the distance between the two endpoints of the diameter using the formula provided. Once you calculate that distance, divide it by 2 to get the radius. The standard equation of the circle can be expressed as
, substituting in your center and radius values.
Finding the area and radius can also help in visualizing problems related to circular motion and forces in physics! Think of it like mapping out a dance floor where the center is the DJ booth, and the radius shows how far the dance moves can go—just watch for those doing the cha-cha at the edges!
When calculating the radius, be sure to avoid common mistakes such as incorrectly determining the distance formula or miscalculating coordinates. It’s all about getting your coordinates right to keep that party in perfect rhythm!

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