Answer:
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.
Answer:
radius = 5 units
Step-by-step 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 = ( [tex]\frac{x3+11}{2}[/tex], [tex]\frac{1+7}{2}[/tex] ) = ([tex]\frac{14}{2}[/tex], [tex]\frac{8}{2}[/tex] ) = (7, 4 )
Using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = C (7, 4 ) and (x₂, y₂ ) = (11, 7 )
r = [tex]\sqrt{(11-7)^2+(7-4)^2}[/tex]
= [tex]\sqrt{4^2+3^2}[/tex]
= [tex]\sqrt{16+9}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
