Radius of the circle with center at (1, 2) and point (-3, 4) on the circle

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.