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:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plug in the given points:

$d=\sqrt{(-2-x_1)^2+(1-y_1)^2}\\d=\sqrt{(-2-6)^2+(1-7)^2}\\d=\sqrt{(-8)^2+(-6)^2}\\d=\sqrt{64+36}\\d=\sqrt{100}\\d=10$

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