Question

A circle is centered at the point (7,1) and passes through the point (8,7). what is the radius

Answer 1

The radius of the circle with center (7,1) and passing through (8,7) is calculated as the distance between the two points, which is √37.

Step-by-step explanation:

To find the radius of a circle that is centered at the point (7,1) and passes through the point (8,7), you need to calculate the distance between these two points. This distance will be the radius of the circle. The distance between two points (x1,y1) and (x2,y2) in the Cartesian plane is given by the formula √((x2-x1)² + (y2-y1)²). So, in this case, the radius is the distance from (7,1) to (8,7), which is √((8-7)² + (7-1)²) = √(1² + 6²) = √1 + 36 = √37.

Answer 2

easy

the radius is the distance from the center to a point on the circle

we are given
center=(7,1)
a point=(8,7)
find the distance
distance formula
D=
`√((x2-x1)^2+(y2-y1)^2)`

so the distance between point and center is radius
D=
`√((8-7)^2+(7-1)^2)`
D=
`√((1)^2+(6)^2)`
D=
`√(1+36)`
D=√37 units


radius is √37 units