Use the distance formula?
To find the length of the radius of a circle when given the endpoints of a diameter, one needs to calculate the distance between the two points and then divide by two.
The distance between two points (-2, -4) and (8, 5) can be found using the distance formula: √((x₂ - x₁)² + (y₂ - y₁)²).
This formula is derived from the Pythagorean theorem, which is used in geometry to calculate the length of the sides of a right triangle.
In this case, the distance d between the points is: √((8 - (-2))² + (5 - (-4))²) = √((10)² + (9)²) = √(100 + 81) = √181.
The radius of the circle is half the diameter, so the length of the radius r is: r = d / 2 = √181 / 2.
The radius of the circle with endpoints of the diameter at (-2, -4) and (8, 5) is 2 181 . This is found by calculating the distance between the points and then dividing by two. The distance is calculated using the distance formula from geometry.
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