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A circle in the xy-plane has its center at the point (0.4,-0.3). If the point (6,5) lies on the circle, what is the diameter of the circle? Round the answer to the nearest tenth. Choose 1 answer: (A) 7.7 units (B) 15.4 units (C) 59.5 units (D) 119 units

A circle in the xy x y -plane has its center at the point (0.4,−0.3) (0.4,-0.3) . If the point (6,5) (6,5) lies on the circle, what is the diameter of the circle? Round the answer to the nearest tenth.\newlineChoose 11 answer:\newline(A) 77.77 units\newline(B) 15.4 15.4 units\newline(C) 5959.55 units\newline(D) 119119 units

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Q. A circle in the xy x y -plane has its center at the point (0.4,−0.3) (0.4,-0.3) . If the point (6,5) (6,5) lies on the circle, what is the diameter of the circle? Round the answer to the nearest tenth.\newlineChoose 11 answer:\newline(A) 77.77 units\newline(B) 15.4 15.4 units\newline(C) 5959.55 units\newline(D) 119119 units
  1. Identify Formula: Identify the formula to calculate the radius of the circle.\newlineThe radius of a circle can be found using the distance formula between two points, which is the center of the circle and a point on the circle.
  2. Use Distance Formula: Use the distance formula to calculate the radius.\newlineThe distance formula is d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, where (x1,y1)(x_1, y_1) is the center of the circle and (x2,y2)(x_2, y_2) is a point on the circle.
  3. Substitute Given Points: Substitute the given points into the distance formula.\newlineCenter: (0.4,−0.3)(0.4, -0.3), Point on circle: (6,5)(6, 5)\newlineRadius =(6−0.4)2+(5−(−0.3))2= \sqrt{(6 - 0.4)^2 + (5 - (-0.3))^2}
  4. Perform Calculations: Perform the calculations to find the radius.\newlineRadius = (5.6)2+(5.3)2\sqrt{(5.6)^2 + (5.3)^2}\newlineRadius = 31.36+28.09\sqrt{31.36 + 28.09}\newlineRadius = 59.45\sqrt{59.45}
  5. Calculate Square Root: Calculate the square root to find the radius.\newlineRadius ≈59.45\approx \sqrt{59.45}\newlineRadius ≈7.71\approx 7.71 (rounded to the nearest tenth)
  6. Double Radius: Double the radius to find the diameter of the circle.\newlineDiameter =2×= 2 \times Radius\newlineDiameter =2×7.71= 2 \times 7.71\newlineDiameter ≈15.42\approx 15.42
  7. Round Diameter: Round the diameter to the nearest tenth.\newlineDiameter ≈15.4\approx 15.4 units

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