Radius of a Circle Given Center and Point
To find the radius of a circle when we're given the coordinates of its center and a point it contains, we can use the following formula for distance:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
- [tex](x_1,y_1)[/tex] is one point and [tex](x_2,y_2)[/tex] is another
Solving the Question
We're given:
- Center: (-2,1)
- Point: (2,-1)
Plug these given points into the formula for distance:
[tex]d=\sqrt{(2-(-2))^2+(-1-1)^2}\\d=\sqrt{(2+2)^2+(-1-1)^2}\\d=\sqrt{(4)^2+(-2)^2}\\d=\sqrt{16+4}\\d=\sqrt{20}\\d\approx4.47[/tex]
Answer
Therefore, the radius of the circle is [tex]\sqrt{20}[/tex] units, or approximately 4.47 units.
