The diameter of a circle has endpoints A(1, 3) and B(4, 7), what is the
circumference of that circle in terms of pi?

The circumference of the circle is 5π

Step-by-step explanation:

First we need to calculate the diameter  

for this we have to know the distance between A(1, 3) and B(4, 7)

X =  Xb - Xa

X = 4 - 1

X = 3

Y = Yb - Ya

Y = 7 - 3

Y = 4

b - a = (3 , 4)

now that we have the distance of x and r we can calculate its distance using Pythagoras

h = hypotenuse

x = leg 1 = 3

y = leg 2 = 4

h² = x² + y²

we replace the known values

h² = (3)² + (4)²

h² = 9 + 16

h² = 25

h = √25

h = 5

The diameter of the circle is 5

Now we need to calculate the circumferencefor this we need to use the circumferenc formula of a circle:

c = circumference

d = diameter = 5

π = pi

c = π * d

we replace with the known values

c = 5  * π

c = 5π

The circumference of the circle is 5π

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