The edges of the diameter of a circle are at (-1,2) and (3,-1). write the equation of the circle in general form.

if anyone can also list the steps it would really be appreciated : ) i'm very lost on this whole subject at the moment haha

(x-1)²+ (y-0.5)²=6.25

Step-by-step explanation:

The standard form of equation of a circle is;

(x-a)²+(y-b)²=r² where (a,b) are the center of the circle and r is the radius

Finding the mid-point of the given points

(-1,2) and (3,-1)⇒midpoint will be 1/2(x₁+x₂) , 1/2(y₁+y₂)

midpoint= {1/2(-1+3), 1/2(2+-1)}

midpoint=(1,0.5)

Finding the radius r; the distance from the center to either of the given two points

Apply the distance formula d=√ (x₂-x₁)² +(y₂-y₁)²

Taking (x₁,y₁) as (1,0.5) and (x₂,y₂) as (-1,2) then

d=√ (-1-1)² +(2-0.5)²

d= √ (-2)²+(1.5)²

d=√4+2.25⇒√6.25⇒2.5

r=2.5

Equation of the circle

(x-1)² + (y-0.5)²=2.5²

(x-1)²+ (y-0.5)²=6.25

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0