Question

The endpoints of the diameter of a circle are (2,1) and (6,5).

A) Radius is 3 units
B) Radius is 5 units
C) Diameter is 4 units
D) Diameter is 6 units

Answer 1

By using the distance formula to find the diameter of the circle with endpoints (2,1) and (6,5), we determine the diameter to be 4√2 units, which approximates closest to 6 units out of the provided options.

Step-by-step explanation:

The question involves finding the length of the diameter of a circle given the endpoints of the diameter. To solve this, we use the distance formula to calculate the distance between the points (2,1) and (6,5), which represent the endpoints of the diameter. The formula is the square root of the sum of the square of the differences of the x-coordinates and the y-coordinates. Calculating, we get
`√([(6-2)^2 + (5-1)^2]) = √([16 + 16] ) = √([32])`, which simplifies to 4√2. Knowing that this distance is the diameter, we find that the radius, which is half the diameter, is 2√2 units. This value is approximately 2.828 units, not precisely 3 units. Therefore, the correct answer must be related to the length of the diameter, as it roughly corresponds to the calculated length of 4√2. Hence, option D, stating that the diameter is 6 units is the closest approximation to our calculated length (as 6 units are a bit less than 4√2), so we consider this the best answer given the available options, acknowledging that the length of the diameter is not exactly 6 units.