Question

What is the length of the radius of a circle with a center at 2 + 3i and a point on the circle at 7 + 2i?

Answer 1

distance between 2 points (radius)
= sqrt( (7-2)^2 + (2-3)^2 ) = sqrt(26)

Answer 2

Length of the radius of a circle =
`√(26)`

Explanation:

a circle with a center at 2 + 3i and a point on the circle at 7 + 2i

To find the length of the radius, find the distance between the center and a point on the circle

center is 2+3i that is (2,3)

point is 7+2i that is (7,2)

distance formula is
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Plug in the values in the formula

Distance=
`√((7-2)^2+(2-3)^2)`

Distance=
`√((5)^2+(-1)^2)`

Distance=
`√((26)`

Length of the radius of a circle =
`√(26)`