Question

What’s the radius of center (-2,1) and contains the point (2,-1)

Answer 1

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:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

• $(x_1,y_1)$ is one point and $(x_2,y_2)$ is another

Solving the Question

We're given:

• Center: (-2,1)
• Point: (2,-1)

Plug these given points into the formula for distance:

$d=\sqrt{(2-(-2))^2+(-1-1)^2}\\d=\sqrt{(2+2)^2+(-1-1)^2}\\d=\sqrt{(4)^2+(-2)^2}\\d=\sqrt{16+4}\\d=\sqrt{20}\\d\approx4.47$

Answer

Therefore, the radius of the circle is $\sqrt{20}$ units, or approximately 4.47 units.