Question

The diameter of a circle has endpoints at (3,1) and (11,7) find the radius

Answer 1

radius = 5 units

Explanation:

The radius r is the distance from the centre to either of the 2 endpoints of the diameter.

Calculate the centre C using the midpoint formula

C = (
`(x3+11)/(2)`,
`(1+7)/(2)` ) = (
`(14)/(2)`,
`(8)/(2)` ) = (7, 4 )

Using the distance formula

r =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = C (7, 4 ) and (x₂, y₂ ) = (11, 7 )

r =
`√((11-7)^2+(7-4)^2)`

=
`√(4^2+3^2)`

=
`√(16+9)`

=
`√(25)`

= 5

Answer 2

the radius of this circle is 5

Step-by-step explanation:

First find the diameter (which is the distance between the two given points). The radius will be half that distance.

Going from (3,1) to (11,7), the x-component increases by 8 (from 3 to 11) and the y-component by 6. The Pythagorean Theorem tells us that the distance between these two points (that is, the hypotenuse) is

d = √(8² + 6²) = √100 = 10. Thus, the radius of this circle is 5.