If the endpoints of a diameter of a circle are (6,2) and (0, 2); what is the radius of
the circle?

The radius of circle is 3

Step-by-step explanation:

Given the endpoints of diameter of a circle are (6,2) and (0,2)

We know that the equation of circle is

+ =

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

To find (h,k): the center is midpoint of diameter

Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by

( , )

( , )

(3, 2)

Hence (h,k) is (3,2)

Substituting values of (h.k) and (x.y) as (3,2) and (0,2) respectively, we get

+ =

=

r =3

Hence the radius of the circle is 3

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so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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