Question

Plz hurryThe center of circle Q has coordinates Q(6,-4) . If circle Q passes through R(14,2) , what is the length of its diameter?

Answer 1

Answer:

the diameter is twice the circle radius, or 20

Step-by-step explanation:

Recall that the radius is half the diameter <=> the diameter is twice the radius.  In this problem we need to find the radius first, then multiply it by 2 to obtain the diameter.

We need to determine the distance between the center of the circle Q(6, -4) and the point R(14, 2) on the circle.  

The Pythagorean Theorem applies here.  Going from Q to R, x changes from 6 to 14, or 8 units, which is the horizontal leg of a right triangle, and y changes from -4 to 2, or 6 units.  Thus, according to the Pythagorean Theorem, the length of the hypotenuse of this triangle is

r = √(6² + 8²) = √100 = 10

and so the diameter is twice that, or 20.