Answer:
To find the length of the radius of the circle when given the endpoints of a diameter, you can use the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the endpoints of the diameter are (-7, -4) and (2, 5).
Let's plug these values into the formula:
Distance = √((2 - (-7))^2 + (5 - (-4))^2)
Distance = √((2 + 7)^2 + (5 + 4)^2)
Distance = √(9^2 + 9^2)
Distance = √(81 + 81)
Distance = √162
Now, simplify the square root:
Distance ≈ 12.73
So, the length of the diameter of the circle is approximately 12.73 units. Since the radius is half of the diameter, the radius is half of 12.73:
Radius ≈ 12.73 / 2 ≈ 6.36
The length of the radius of the circle is approximately 6.36 units.