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40 votes
40 votes
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?

User RmIu
by
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1 Answer

8 votes
8 votes

Answer:

the diameter is twice the circle radius, or 20

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.

User Dheeraj Bhaskar
by
2.8k points
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