P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
The correct answer is A. 6.5 units
The distance between the endpoints of a diameter of a circle is equal to the diameter of the circle.
Given points P(-6, 1) and Q(6, 6), we can use the distance formula to find the length of the diameter:
Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Distance = \(\sqrt{(6 - (-6))^2 + (6 - 1)^2}\)
Distance = \(\sqrt{12^2 + 5^2}\)
Distance = \(\sqrt{144 + 25}\)
Distance = \(\sqrt{169}\)
Distance = 13 units.
Since the diameter is twice the radius, the radius of the circle is half of the diameter:
Radius = \(\frac{13}{2} = 6.5\) units.
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