Final answer:
In this case, the other endpoint of the diameter is (11, 11).
Step-by-step explanation:
To find the other endpoint of the diameter, we can use the information given about the center and radius of the circle.
Let's start by plotting the given points on a coordinate plane. The center of the circle is given as C(7, 8), and one endpoint of the diameter is (3, 5).
To find the other endpoint, we can use the fact that the center of the circle is the midpoint of the diameter.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
Using this formula, we can find the x-coordinate of the other endpoint:
x-coordinate of midpoint = (x-coordinate of endpoint 1 + x-coordinate of endpoint 2) / 2
Substituting the known values:
7 = (3 + x-coordinate of endpoint 2) / 2
Solving for x-coordinate of endpoint 2:
- 7 = (3 + x-coordinate of endpoint 2) / 2
- 14 = 3 + x-coordinate of endpoint 2
- x-coordinate of endpoint 2 = 14 - 3
- x-coordinate of endpoint 2 = 11
Now, let's find the y-coordinate of the other endpoint:
y-coordinate of midpoint = (y-coordinate of endpoint 1 + y-coordinate of endpoint 2) / 2
Substituting the known values:
8 = (5 + y-coordinate of endpoint 2) / 2
Solving for y-coordinate of endpoint 2:
- 8 = (5 + y-coordinate of endpoint 2) / 2
- 16 = 5 + y-coordinate of endpoint 2
- y-coordinate of endpoint 2 = 16 - 5
- y-coordinate of endpoint 2 = 11
Therefore, the other endpoint of the diameter is (11, 11).
Your question is incomplete, but most probably the full question was:
C (7, 8) is the center of the circle having a radius = 5 units. A diameter is drawn on this circle, and one of its endpoints is (3, 5). Find the other endpoint, please provide an in-depth explanation for future reference to similar problems.