Circle Q has a diameter WY. Point W is located at (3, −2), and point Y is located at (5, −6). Which of the following ordered pairs represents point Q, the center of the circle? F (8, −8) G (4, −4) H (−1.5, 1.5) J (3, −6)

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Circle Q has a diameter WY. Point W is located at (3, −2), and point Y is located at (5, −6). Which of the following ordered pairs represents point Q, the center of the circle? F (8, −8) G (4, −4) H (−1.5, 1.5) J (3, −6)

Mathematics
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G
Since the diameter is the chord passing the center of the circle, you know that segment WQ is congruent to segment YQ. This means you must find the midpoint of the diameter using the given points. Midpoint coordinate for X = (x1+x2) / 2 (average of given x coordinates of W and Y). Midpoint coordinate for Y = (y1+y2) / 2 (average of given y coordinates of W and Y).
The final answer is calculated by plugging in the values to the midpoint formulas. Mid point x coordinate = (5+3) /2 = 8 /2 = 4 Mid point y coordinate = (-2-6) /2 = -8 /2 = -4 So the center of the diameter (also known as the midpoint of the diamenter) is (4,-4). Answer G is correct.

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