Question

The center of circle Q has coordinates (3,-2). If circle Q passes through R(7,1), what is the

length of its diameter?
A. 50
B. 25
C. 10
D. 5

Answer 1

C.

Explanation:

We can use the distance formula to find the distance between the center of circle Q and point R, which is also the radius of the circle. Then, we can multiply this value by 2 to get the diameter of the circle.

Distance Formula:

The distance between two points with coordinates (x1, y1) and (x2, y2) is given by the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the distance formula, we can find the radius of circle Q:

radius = sqrt((7 - 3)^2 + (1 - (-2))^2)

= sqrt(4^2 + 3^2)

= 5

Therefore, the diameter of the circle is:

diameter = 2 * radius

= 2 * 5

= 10

So, the length of the diameter of circle Q is 10 units.