Find the radius of the circle if the center is at (1, 2) and the point (-3, 4) lies on the circle.
4 units
4.25 units
4.47 units
20 units
Radius of the circle with center at (1, 2) and point (-3, 4) on the circle
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To find the radius of the circle given the center at (1, 2) and a point (-3, 4) on the circle, we can use the distance formula. The radius is the distance between the center and the point on the circle:
The distance ( d ) is calculated as:
[
d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
Substituting the coordinates:
– Center ((x_1, y_1) = (1, 2))
– Point ((x_2, y_2) = (-3, 4))
The calculation becomes:
[
d = sqrt{((-3) – 1)^2 + (4 – 2)^2}
]
[
d = sqrt{(-4)^2 + (2)^2}
]
[
d = sqrt{16 + 4} = sqrt{20} approx 4.47 text{ units}
]
So, the radius of the circle is approximately 4.47 units.