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The center of circle o has coordinates (3,-2). If circle passes through R(7,1), what is the length of its diameter?

Answer 1

James Atkins

#10#

Given that Circle #O# is centered at (3,-2) and the circle passes through #R(7,1)#,

The distance between #O and R# is the radius #(r)#.

#r=sqrt((7-3)^2+(1-(-2))^2)=sqrt25=5#

diameter #=2*r =2*5=10#

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Answer 2

Carson Arnold

Using the distance formula, the distance between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is given by:

[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

Given that the center of the circle is at ( (3, -2) ) and it passes through ( (7, 1) ), the distance between these two points will be the diameter of the circle. Thus, substituting the coordinates into the distance formula:

[ d = \sqrt{(7 - 3)^2 + (1 - (-2))^2} ]

[ d = \sqrt{(4)^2 + (3)^2} ]

[ d = \sqrt{16 + 9} ]

[ d = \sqrt{25} ]

[ d = 5 ]

Therefore, the length of the diameter of the circle is 5 units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.