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=√((2-(-2))^2+(-1-1)^2)\\d=√((2+2)^2+(-1-1)^2)\\d=√((4)^2+(-2)^2)\\d=√(16+4)\\d=√(20)\\d\approx4.47`

Answer

Therefore, the radius of the circle is
`√(20)` units, or approximately 4.47 units.