Find the circumference of a circle whose diameter has endpoints at (2 , 1) and (4 , 5).
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You need to remember that the endpoints of diameter lie on circle. Since you know coordinates of endpoints of diameter you may evaluate how long it is such that:`d=sqrt((2-4)^2+(1-5)^2)` .
`d=sqrt((-2)^2+(-4)^2) =gt d=sqrt(4+16) =gt d=sqrt20` `=gt d=sqrt(2^2*5)=gtd=2sqrt5`
Since the formula of circumference comprises the length of radius of circle, hence you may find the radius as half of diameter length.
`r=d/2=gtr=sqrt5`
You may evaluate circumference of circle such that:
circumference=`2r*pi `
Substituting `sqrt5` for r yields: circumference=`2sqrt5*pi` .
Hence, evaluating the circumference of circle yields circumference=`2sqrt5*pi ` units.
Related Questions
- Calculate the circumference and area of the circle whose diameter = 14.
- 2 Educator Answers
- What is the area of the circle if the diameter has endpoints (2,7) and (-4, -1).
- 1 Educator Answer
- Write the equation of a circle with endpoints of the diameter at (2, -5) and (-4, 3)
- 1 Educator Answer
- What is the ratio of the circumferences of two circles that have diameters in the ratio 1:5 ?
- 2 Educator Answers
- What is the circumference of the circle whose area is 25pi ?
- 2 Educator Answers
Find the circumference of a circle whose diameter has endpoints at (2 , 1) and (4 ,5).
First, remember that the formula for circumference is: C=2*pi*r, or C=pi*d, where d=diameter of circle.
The distance between the given points can be determined by using the formula:
Distance=Square root of [(difference in x values)^2 + (difference in y values)^2]
Substituting the given values, Distance= square root of [(4-2)^2 + (5-1)^2]
Distance = square root of [2^2 + 4^2]
Distance = square root of (4 + 16)
Distance = square root of 20
Distance = 2*square root of 5
now substituting into the circumference formula,
Circumference = 2*square root of 5*pi;
to expand further, you have 2*2.236*3.143=14.0555 (all approximate values)
C = pi*D, where D is the diameter of the circle.
We'll calculate the length of the diameter using the formula:D = sqrt[(4-2)^2 + (5-1)^2]
D = sqrt (4 + 16)D = 2sqrt5
The circumfrence of the circle whose diameter has endpoints at (2 , 1) and (4 , 5) is: C = 2pi*sqrt5.
Student Answers