Right triangle ABC is located at A (-1.4), B (-1, 1), and C (-5. 1) on a coordinate plane. What is the equation of a circle A with radius AC (x + 1)2 + y - 4)2 = 9
x + 5)2 + y - 1)2 = 25
(x + 5)² + (y - 12 = 16
x + 1)2 + y - 42 = 25

The equation of circle A with radius AC is , or in other words option d.

Step-by-step explanation:

If the radius of this circle is AC, then we can determine the distance between points A ( - 1, 4 ) and C ( - 5,1 ) to come to the length of the radius -

Distance between A and C =

=

= = = 5 units - Which is also the length of the radius of the circle.

So if the radius is given to be 5 in length, knowing that the general equation for a circle is ( where ( h, k ) is the center and r is the radius ) if the radius is 5, , and solution must be option b / option d.

Now if the radius is AC, the center point must be point A ( circle A ). Therefore point ( - 1, 4 ) is the center, and the equation of the circle must be the following -

= - and hence our solution is option d

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step-by-step explanation: