The endpoint of a diameter of a circle are L(-3,-2) and G(9,-6) what is the length of the radius of the circle?
The endpoints of a diameter of a circle are L(-3,-2) and G(9,-6). what is the length of the radius of the circle
Use the Distance Formula. then divide the answer by 2 to get the radius.
To find the length of the radius of the circle, we first need to find the center of the circle.
Step 1: Find the midpoint of the diameter.
The midpoint of the diameter can be found by taking the average of the x-coordinates and y-coordinates of the endpoints.
The x-coordinate of the center is (-3 + 9) / 2 = 6 / 2 = 3.
The y-coordinate of the center is (-2 + (-6)) / 2 = -8 / 2 = -4.
So, the center of the circle is C(3, -4).
Step 2: Find the distance between one of the endpoints and the center.
We can use the distance formula to find the length of the radius.
The distance formula is given by: d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
Using C(3, -4) as the center and L(-3, -2) as one of the endpoints, the formula becomes:
d = sqrt(((-3) - 3)^2 + ((-2) - (-4))^2)
= sqrt((-6)^2 + (2)^2)
= sqrt(36 + 4)
= sqrt(40)
= 2 * sqrt(10).
Therefore, the length of the radius of the circle is 2 * sqrt(10).
To find the length of the radius of a circle given the coordinates of its endpoints of a diameter, we can use the distance formula. The distance formula is derived from the Pythagorean theorem. It states that the distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by:
d = √[(x2 - x1)² + (y2 - y1)²]
In this case, L (-3, -2) represents (x1, y1) and G (9, -6) represents (x2, y2). Let's proceed with calculating the distance:
d = √[(9 - (-3))² + (-6 - (-2))²]
= √[(9 + 3)² + (-6 + 2)²]
= √[12² + (-4)²]
= √[144 + 16]
= √160
≈ 12.65
Therefore, the length of the radius of the circle is approximately 12.65 units.