Question

The center of circle q has coordinates (-2, 1). if circle q passes through r (6, 7), what is the length of its diameter?

Answer 1

Diameter of a Circle

There are multiple strategies we can use to find the diameter of a circle. For this question, we must calculate the length of the radius first and multiply by 2 to find the diameter.

Solving the Question

We're given the centre and a point on the circumference:
`(-2,1),(6,7)`.

Find the distance between them using the distance equation:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Plug in the given points:

`d=√((-2-x_1)^2+(1-y_1)^2)\\d=√((-2-6)^2+(1-7)^2)\\d=√((-8)^2+(-6)^2)\\d=√(64+36)\\d=√(100)\\d=10`

Therefore, the radius of the circle is 10 units.

Multiply the radius by 2 to find the length of the diameter:

10 × 2

= 20

Therefore, the length of the diameter is 20 units.

Answer

20 units